<html><body><div style="font-family: arial, helvetica, sans-serif; font-size: 12pt; color: #000000"><div><br></div><div>Yaygın olarak bilinmeyen ve Türkiye'de daha az bilindiğini tahmin ettiğim real induction adlı kavramla ilgili temel bir makalenin linki: </div><div> <a href="http://alpha.math.uga.edu/~pete/instructors_guide_shorter.pdf">http://alpha.math.uga.edu/~pete/instructors_guide_shorter.pdf</a><br data-mce-bogus="1"></div><div><br data-mce-bogus="1"></div><div>Reel sayılarda real induction tamlık aksiyomuna denk olup calculusun hemen hemen bütün temel teoremleri kanıtlanabiliyor. Örneğin,  kapalı ve sınırlı aralıkta tanımlı </div><div>sürekli her fonksiyonun bu kavramın kullanılmasıyla verilen kanıtıyla, seçim aksiyomu kullanılarak ya da kullanılmadan verilen kanıtların karşılaştırılması</div><div>kullanılan kavramların daha net anlaşılmasını sağlayacağını düşünüyorum.   </div><div><br data-mce-bogus="1"></div><div>Bu arada her kümenin seçim fonksiyonu olan bir kümeyle eşleşebiliyor olmasının pratiksel karşılığının ne olabileceğini kestiremiyorum.</div><div><br data-mce-bogus="1"></div><div>ZE</div><div><br></div><hr id="zwchr" data-marker="__DIVIDER__"><div data-marker="__HEADERS__"><b>From: </b>"Burak Kaya" <burakk@metu.edu.tr><br><b>To: </b>"Ali Nesin" <anesin@nesinkoyleri.org>, "tmd" <tmd-uye@listweb.bilkent.edu.tr><br><b>Sent: </b>Monday, December 2, 2024 8:16:34 PM<br><b>Subject: </b>[TMD-UYE: 4243] Re: [Turkmath:6800] karadeniz aklı.. çalışmıyor 12 den sonra... Ek i eklemeyi unutmuşum...<br></div><div><br></div><div data-marker="__QUOTED_TEXT__"><p>Hocam aslında öne sürdüğünüz prensip Seçim Beliti lehine
      yorumlanabilir:</p>
    <p>Belitlerimiz dahilinde "olabildiğince az küme olmalı" prensibiyle
      hareket edersek*, Gödel'in inşa edilebilirlik beliti V=L'yi bir
      belit olarak almalıyız zira Gödel'in inşa edilebilir evreni L,
      ZF'nin modeli olan en küçük iç model (Diğer bir deyişle, V'nin tüm
      ordinalleri içeren bir alt sınıfı M eğer ZF belitlerini
      sağlıyorsa, bu durumda L \subseteq M olmalı.) Ancak L içerisinde
      Seçim Beliti'nin (ve Genelleştirilmiş Süreklilik Hipotezi'nin)
      doğru olduğunu kanıtlayabiliyoruz. Dolayısıyla "ZF'nin bir modeli
      olsun ama içerisine gereksiz kümeler koymayalım, olabildiğince az
      kümeyle bir model elde edelim" dediğimizde Seçim Beliti doğru
      olmak zorunda kalıyor. Sınıf modellerle değil küme modellerle
      çalışırsak da, yine, ZF'nin eğer bir geçişken standart modeli
      varsa, minimal bir standart geçişken modeli var, Shepherdson
      modeli. Bu model de V=L'yi sağladığı için Seçim Beliti, GCH,...
      doğru oluyor:
      <a href="https://en.wikipedia.org/wiki/Minimal_model_%28set_theory%29" target="_blank" rel="nofollow noopener noreferrer">https://en.wikipedia.org/wiki/Minimal_model_(set_theory)</a><br>
    </p>
    <p>İyi çalışmalar,</p>
    <p>Burak Kaya<br>
    </p>
    <p>*: Bu arada bir takım küme kuramcılarının yaklaşımı bunun tam
      tersi, yani bir tür "maximality principle" benimsemek,
      olabildiğince çok ve farklı kümeler koymak. Ben bireysel olarak
      Platonist bir tek evren görüşü yerine küme kuramsal çoklu
      evrenlere daha yakın olduğumdan, Seçim Beliti "gerçekte" doğru mu
      değil mi çok üzerine düşünmüyorum; diğer yandan, pratik matematik
      için bir gereklilik olduğu bence aşikar.<br>
    </p>
    <div class="moz-cite-prefix">On 12/2/2024 7:38 PM, Ali Nesin wrote:<br>
    </div>
    <blockquote>
      
      <p>Biraz felsefe yapayım.</p>
      <p>Bir kümeler kuramının bir modelinde doğduğumuzu varsayıyorum.
        Matematiğin içinde yaşadığımız evreni anlamaya yettiğini
        düşünüyorsak, buna da inanmak zorundayız galiba.</p>
      <p>Soru: Hangi kuramda ve hangi modelde?</p>
      <p>Doğada en az enerji yasası vardır, birçok yerde geçerlidir bu,
        insanlarda bile! Bu ilkeden hareketle, içinde doğduğumuz
        modelde, evrenin var olmasında bir rolü olmayan ve/ya da evreni
        anlamamıza yardımcı olmayan topluluklar küme olmamalıdır. Sonuç:
        Seçim Aksiyomu bal gibi içinde doğduğumuz modelde yanlış
        olabilir! Aynı gerekçeyle Süreklilik Hipotezi de doğru olmalı!</p>
      <p>A</p>
      <p><br>
      </p>
      <p><br>
      </p>
      <div class="moz-cite-prefix">02.12.2024 15:27 tarihinde Burak Kaya
        yazdı:<br>
      </div>
      <blockquote>
        
        <p>Sayın Zafer hocam,</p>
        <p>Seçim belitini hangi matematikçiler reddediyor (ya da sizin
          deyiminizle hangi matematikçiler bu belitle kavga ediyor) emin
          değilim ama böyle matematikçiler varsa reddettiklerini
          söylediklerini şey hakkında muhtemelen pek bilgileri yok:
          Seçim beliti olmadan sadece ZF içerisinde çok şey yapmak pek
          mümkün değil. Analizi temel seviyede geliştirebilmek için
          bile, örneğin Lebesgue ölçüsünün sayılabilir toplamsallığını
          kanıtlamak için, seçim belitinin basit bir formu (örneğin DC,
          dependent choice) gerekli. (Zira ZF+"Gerçel sayılar
          sayılabilir tane sayılabilir kümenin birleşimidir" teorisi
          tutarlı.) Ya da sonsuz bir kümenin sayılabilir sonsuz bir
          altkümesi olduğunu söyleyebilmek için seçim belitinin basit
          bir formu (örneğin CC, countable choice). Bunun gibi onlarca
          örnek sıralanabilir... Dolayısıyla seçim belitinin DC ya da CC
          gibi basit formlarını bile kullanmadığını söyleyen bir
          matematikçi ya tamamen sonlucu bir matematik yapıyordur ya
          inşacı bir yaklaşım benimsemiştir ya da sezgisel olarak
          yaptığı argümanlar küme kuramsal bir sisteme aktarıldığında
          hangi belit gerekecek bilmiyordur.</p>
        <p>Artık 1900'lerin ilk yarısında yaşamıyoruz. Seçim belitiyle
          ilgili pek çok şey çözülmüş durumda, yurt dışındaki
          matematikçiler ve küme kuramcıları arasında da bununla ilgili
          pek bir "tartışma" olduğuna rastlamadım. Seçim belitinin ne
          zaman gerekip gerekmediğini öğrenmek isteyen ve belitle ilgili
          daha çok şey öğrenmek isteyen birisi sizin de referansını
          verdiğiniz <b>Herrlich'in "Axiom of Choice"</b> ve <b>Jech'in
            "The Axiom of Choice"</b> kitaplarını okuyabilir. Bunlar
          artık klasikleşmiş kitaplar.<br>
        </p>
        <p>Bunun dışında bir iki düzeltme yapmak istiyorum:</p>
        <ul><li>Fermat'nın son teoremi matematiksel mantıkçıların
            aritmetik önerme dediği türden bir önerme. Shoenfield
            mutlaklık teoreminin bir sonucu şu: Karmaşıklığı
            Sigma_2^1/Pi_2^1 olan bir önerme (ki böyle önermeler
            aritmetik önermeleri kapsar) eğer seçim beliti kullanılarak
            kanıtlanabiliyorsa, seçim beliti kullanılmadan da
            kanıtlanabilir. Dolayısıyla Fermat'nın son teoremini seçim
            beliti kullanmadan kanıtlamak mümkün. Ana fikir şu: Tüm
            argümanı Gödel'in inşa edilebilir evreni L içerisinde seçim
            beliti kullanmadan gerçekleştirebiliriz zira seçim belitinin
            L'de doğru olduğu bir aksiyom değil, bir teorem. Bu durumda
            teoremin ifadesinin "L'ye relativizasyonunu" ZF içerisinde
            kanıtlamış olacağız. Ancak Shoenfield mutlaklık teoreminden
            dolayı bu önerme L'de doğruysa kümeler evreni V'de de
            doğrudur.</li><li>Köşe yazınızda Süreklilik Hipotezi'ni sanki Hilbert 23
            probleminde ortaya attı gibi bir algı ortaya çıkıyor ama
            sizin de bildiğiniz üzere bu hipotez Cantor tarafından
            ortaya atılıyor. Hilbert 23 problemini ifade ederken 1.
            problemi olan Cantor'un süreklilik problemine ilişkin
            yazdığı kısmın ikinci yarısında bu problemin çözümüyle
            alakalı olduğunu düşündüğü bir problem olarak gerçel
            sayıların bir iyi sıralamasını bulma probleminden
            bahsediyor. Ancak Hilbert'in ifadesi gerçel sayıların iyi
            sıralamalarını bulmakla kısıtla, her kümenin iyi
            sıralamasını bulmakla değil. Dolayısıyla Hilbert'in bu
            problemleri ortaya koyarken Zermelo'nun iyi sıralama teoremi
            gibi bir şeyi düşündüğünden emin değilim: <a href="https://www.ams.org/journals/bull/2000-37-04/S0273-0979-00-00881-8/S0273-0979-00-00881-8.pdf" target="_blank" rel="nofollow noopener noreferrer">
https://www.ams.org/journals/bull/2000-37-04/S0273-0979-00-00881-8/S0273-0979-00-00881-8.pdf</a></li><li>Cantor 1874 makalesinde sadece rasyonel sayıların değil
            gerçel cebirsel sayıların sayılabilir olduğunu kanıtlıyor.
            Hatta bunun sonucunda transandantal sayı üretmek için bir
            süreç de ortaya koymuş oluyor. Kitaplar Cantor'un
            yaptıklarını aktarırken bu detayı atladığı için fırsat
            bulmuşken belirtmek istedim.</li></ul>
        <p>Ana konuya dönersek... Seçim belitini kim neden reddediyor
          bilmiyorum ama bugüne kadar seçim belitine karşı makul bir
          argüman duymadım.</p>
        <ul><li>Eğer Banach-Tarski paradoksu sizi rahatsız ediyorsa,
            Banach-Tarski paradoksunu ZF+Hahn-Banach teoremi içerisinde
            de kanıtlamak mümkün (<a href="https://eudml.org/doc/211871" target="_blank" rel="nofollow noopener noreferrer">https://eudml.org/doc/211871</a>).
            Dolayısıyla Banach-Tarski paradoksunu çöpe atmak isteyen
            birisi analizin temel taşlarından birisini de çöpe atmalı.
            Kaldı ki Hahn-Banach teoremi seçim belitinden daha güçsüz
            bir önerme. Yani Banach-Tarski paradoksu için seçim
            belitinin tüm gücüne gerek yok.<br>
          </li><li>Eğer ölçülemez kümeler sizi rahatsız ediyorsa,
            ZF+DC+"Gerçel sayıların her alt kümesi Lebesgue ölçülebilir"
            belitleriyle "R kümesinin öyle bir A parçalanışı (partition)
            vardır ki A'nın kardinalitesi R'den daha büyüktür" önermesi
            kanıtlanabiliyor. Bence bir kümeyi sahip olduğu eleman
            sayısından daha çok sayıda parçaya ayırabilmek ölçülemez
            kümelerden daha patolojik bir şey değil. (<a href="https://mathoverflow.net/questions/260057/axiom-of-choice-banach-tarski-and-reality/260118#260118" target="_blank" rel="nofollow noopener noreferrer">https://mathoverflow.net/questions/260057/axiom-of-choice-banach-tarski-and-reality/260118#260118</a>)</li><li>Eğer her kümenin iyi sıralanabileceği önermesi size çok
            sezgi dışı geliyorsa, kanıtı ZF'de yapılabilen Hartogs
            teoremini okuyun. Herhangi X kümesi için bu X kümesine
            gömülmeyen bir α ordinali olduğunu kanıtlayabiliyorsunuz.
            Ancak bunun ardındaki sezgiyi anladığınızda şu resim
            karşınıza çıkıyor: Eğer α'yı X'e gömemiyorsam, bunun tek
            yolu α'nın elemanlarını X'in elemanlarıyla tek tek sayarken
            bir noktada X'in elemanlarını "bitirmiş" olmam lazım, bunu
            yaptığım en küçük nokta da X'e karşılık gelen
            ordinal/kardinal sayı olmalı. Bu tabii ki X'in iyi
            sıralanabileceğinin bir kanıtı değil, zaten olamaz da zira
            bu seçim beliti olmadan yapılamaz. Diğer taraftan "herhangi
            iki küme verildiğinde birinden diğerine birebir bir
            fonksiyon vardır" ifadesini aksiyom olarak alırsanız, X
            kümesi Hartogs sayısına gömülmek zorunda olacağından
            otomatik olarak iyi sıralanacak. Diğer bir deyişle, bu kanıt
            perspektifinden bakarsanız bir kümeyi iyi sıralamak çok da
            şaşırtıcı çok da matah bir şey değil. Altı üstü seçim
            belitinin bir küme diğerine gömülemiyorsa, diğeri bu kümeye
            gömülmek zorundadır formunu kullanıyor, ki bu formun
            sezgiselliği de bariz olmalı.</li></ul>
        <p>En başa dönersek... Seçim belitine karşı çıkan matematikçiler
          kim bilmiyorum ama önce konudaki halihazırdaki bilgilerini
          daha sonra da argümanlarını duymak isterim.</p>
        <p>Bunun dışında, seçim belitinin lisansta öğretilip
          öğretilmemesinin önemli olduğunu düşünmüyorum. Sonuçta
          yerleştirme belitini (replacement axiom) kaç tane matematikçi
          ifade edebilir? %0.1? Öte yandan ZFC'nin asıl gücü yerleştirme
          belitinden geliyor... Ama matematikçiler yerleştirme belitinin
          ne olduğunu bilmeden hala matematik yapmaya devam edebiliyor,
          değil mi? Pekala matematikçiler, 100 yıldır olduğu gibi, seçim
          belitinin ne olduğunu bilmeden matematik yapmaya devam
          edebilirler. Farkında olmadan kullanacaklar, kullanmak
          zorundalar. Ama yanlış bir şey yapmadıkları sürece, diğer
          belitler ve mantık kuralları gibi, kullandıklarının farkında
          olmaları gerekmiyor. Bu belitlerin amacı zaten bir
          matematikçinin temel sezgisini formalize etmek,
          matematikçilerin amacı gökten zembille inen ZFC'ye tam olarak
          uyup neyi nerede kullandığının farkında olmak değil.<br>
        </p>
        <p>Bundan önemlisi bence lisansta öğrencilere ZFC'den bağımsız
          olan önermeler olduğunu anlatmak. Örneğin, profesyonel
          matematikçiler saygın dergilerde genelleştirilmiş süreklilik
          hipotezinin (GCH) sonuçlarını "basit küme kuramsal gerçekler"
          olarak kullanıp makale basabiliyorlar. Seçim belitini çoğunluk
          kabul ettiği için farkında olmadan kullanmakta sorun yok da,
          CH ya da GCH gibi önermeler böyle şeyler değil. Burada
          farkındalık artırmak düzgün süreklilik kanıtında seçim beliti
          kullandık mı kullanmadık mı farkındalığı artırmaktan daha
          önemli diye düşünüyorum.</p>
        <p>Seçim belitiyle ilgili TMD e-posta tartışması nasıl ve ne
          için başladı emin değilim ama tekerleği (küme kuramcıların 20.
          yüzyılda çoktan çözüp ilerlediği şeyleri) yeniden keşfetmemize
          gerek yok.<br>
        </p>
        <p>Herkese iyi çalışmalar,</p>
        <p>Burak Kaya<br>
        </p>
        <div class="moz-cite-prefix">On 2.12.2024 14:25, Zafer ERCAN
          wrote:<br>
        </div>
        <blockquote>
          <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:#000000">
            <div><br>
            </div>
            <div><br>
            </div>
            <div>Yılmaz hocam,</div>
            <div><br>
            </div>
            <div>Dikkatimi çekti: limitin tanımı epsilon-delta üzerinden
              verilirken seçim aksiyomu kullanılıyor, yanılıyor muyum?
              Bu, seçim aksiyomunu mümkün olduğu kadar reddetme </div>
            <div>eğiliminde olan sert matematikçiler için çok alan
              daraltıcı - armutun sapı üzümün çöpü - bir durum. </div>
            <div><br>
            </div>
            <div>Ayrıca, Fermat'ın son theoremini kanıtlayan Andrew
              Wiles da kanıtını seçim aksiyomunu kullanarak veriyor.</div>
            <div><br>
            </div>
            <div>Şükürler olsun ki Pisagor teoreminin kanıtında seçim
              aksiyomu kullanılmıyor.</div>
            <div><br>
            </div>
            <div>En iyisi seçim aksiyomuyla kavga etmemek! </div>
            <div><br>
            </div>
            <div>ZE </div>
            <hr id="zwchr">
            <div><b>From: </b>"yilmaz
              akyildiz" <a href="mailto:yilmaz.akyildiz@gmail.com" target="_blank" rel="nofollow noopener noreferrer">
                <yilmaz.akyildiz@gmail.com></a><br>
              <b>To: </b>"Zafer ERCAN" <a href="mailto:zercan@ibu.edu.tr" target="_blank" rel="nofollow noopener noreferrer">
                <zercan@ibu.edu.tr></a><br>
              <b>Cc: </b>"Ayşe Uyar" <a href="mailto:ayseu@gazi.edu.tr" target="_blank" rel="nofollow noopener noreferrer">
                <ayseu@gazi.edu.tr></a>, "Ali Nesin" <a href="mailto:anesin@nesinkoyleri.org" target="_blank" rel="nofollow noopener noreferrer"> <anesin@nesinkoyleri.org></a>,
              "Mustafa Polat" <a href="mailto:mpolat@yeditepe.edu.tr" target="_blank" rel="nofollow noopener noreferrer"> <mpolat@yeditepe.edu.tr></a>,
              "turkmath" <a href="mailto:turkmath@listweb.bilkent.edu.tr" target="_blank" rel="nofollow noopener noreferrer">
                <turkmath@listweb.bilkent.edu.tr></a>, "tmd" <a href="mailto:tmd-uye@listweb.bilkent.edu.tr" target="_blank" rel="nofollow noopener noreferrer">
                <tmd-uye@listweb.bilkent.edu.tr></a>, "Zafer
              ERCAN" <a href="mailto:Zafer.Ercan@listweb.bilkent.edu.tr" target="_blank" rel="nofollow noopener noreferrer">
                <Zafer.Ercan@listweb.bilkent.edu.tr></a><br>
              <b>Sent: </b>Monday, December 2, 2024 12:06:37 PM<br>
              <b>Subject: </b>Re: [Turkmath:6800]
              karadeniz aklı.. çalışmıyor 12 den sonra... Ek i eklemeyi
              unutmuşum...<br>
            </div>
            <div><br>
            </div>
            <div>
              <div dir="ltr">
                <div class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"> işte</div>
                <div class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"> işte</div>
                <div class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"> böyle böyle </div>
                <div class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"> bu gibi
                  abstract ve o seviyelerde anlaşılamayacak konularla
                  meşgul ederek,</div>
                <div class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"> epsilon -
                  delta ispatları da buna dahil</div>
                <div class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"> matematikçi
                  olmak için can atan öğrencileri </div>
                <div class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"> fizik veya
                  mühendisliklere kaptırıyoruz</div>
              </div>
              <br>
              <div class="gmail_quote gmail_quote_container">
                <div dir="ltr" class="gmail_attr">On Mon, Dec 2, 2024 at
                  11:33 AM Zafer ERCAN <<a href="mailto:zercan@ibu.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">zercan@ibu.edu.tr</a>>
                  wrote:<br>
                </div>
                <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb( 204 , 204 , 204 );padding-left:1ex">
                  <div>
                    <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                      <br>
                      <div>Kapali ve sırlı aralığın kompakt olduğuda
                        dahil olmak üzere bu ve benzeri yirmiye yakın
                        temel Calculus teoremlerinin kanıtı P. Calrk'ın
                        ''Real induction (2010)'' makalesinde ve Honors
                        Calculus ders notunda var. Bu tür kanıtların
                        daha öncesine Clark'ın bu notlarındaki  referans
                        izlriyle ulaşılabilir.</div>
                      <br>
                      <div>Ayşe hanım, kitabınızın pdf'ini gönderebilir
                        misiniz?</div>
                      <br>
                      <div>ZE</div>
                      <br>
                      <hr id="m_1830330970004194533zwchr">
                      <div><b>From: </b>"Ayşe Uyar" <<a href="mailto:ayseu@gazi.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">ayseu@gazi.edu.tr</a>><br>
                        <b>To: </b>"Ali Nesin" <<a href="mailto:anesin@nesinkoyleri.org" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">anesin@nesinkoyleri.org</a>><br>
                        <b>Cc: </b>"Zafer ERCAN" <<a href="mailto:zercan@ibu.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">zercan@ibu.edu.tr</a>>,
                        "Mustafa Polat" <<a href="mailto:mpolat@yeditepe.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">mpolat@yeditepe.edu.tr</a>>,
                        "yilmaz akyildiz" <<a href="mailto:yilmaz.akyildiz@gmail.com" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">yilmaz.akyildiz@gmail.com</a>>,
                        "turkmath" <<a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">turkmath@listweb.bilkent.edu.tr</a>>,
                        "tmd" <<a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">tmd-uye@listweb.bilkent.edu.tr</a>>,
                        "Zafer ERCAN" <<a href="mailto:Zafer.Ercan@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">Zafer.Ercan@listweb.bilkent.edu.tr</a>><br>
                        <b>Sent: </b>Monday, December 2, 2024 4:09:31
                        AM<br>
                        <b>Subject: </b>Re: [Turkmath:6800]
                        karadeniz aklı.. çalışmıyor 12 den sonra... Ek i
                        eklemeyi unutmuşum...<br>
                      </div>
                      <br>
                      <div>
                        <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                          <div>Kapalı ve sınırlı bir aralıkta sürekli
                            fonksiyonun düzgün sürekli olduğunu seçim
                            aksiyomunu ve kompaktlığı/tıkızlığı
                            kullanmadan kanıtlayabiliriz. "Tek
                            değişkenli analiz" adlı kitabımızda kanıtını
                            vermiştik. Kanıtı kısaca özetleyeyim: </div>
                          <br>
                          <div>f, [a, b] aralığında sürekli ve E={t\in
                            [a,b]: f, [a,t] aralığında düzgün sürekli}
                            olsun. </div>
                          <div>1. adım: E boş kümeden farklıdır. </div>
                          <div>2. adım:  supE=c ise c\in E </div>
                          <div>3. adım: c=b dir.  <br>
                            <br>
                            Kanıt biraz uzun oluyor ancak lisans 1.
                            sınıf öğrencisine seçim aksiyomuna ve açık
                            örtü kavramına girmeden bir kanıt
                            sunabiliyorsunuz. Seçim aksiyomu ve
                            kompaktlık kavramlarının lisansın 3. veya 4.
                            sınıflarında verilmesini daha uygun
                            buluyorum. 1. sınıf analiz dersinde, her ne
                            kadar "tadımlık" Lebesque integralinden
                            bahsetsem de, sürekli fonksiyonların Riemann
                            integrallenebilirliğini kanıtlamak için
                            düzgün süreklilikten faydalanırdım. Bu
                            nedenle, 1. sınıf öğrencilerine seçim
                            aksiyomu ve kompakt uzay kavramı
                            kullanılmadan düzgün süreklilikten <span style="font-size:12pt">bahsedilmesi
                              gerektiğini düşünüyorum. </span>
                            <div><span style="font-size:12pt"> </span></div>
                          </div>
                          <div>Ayşe Uyar <br>
                             </div>
                          <br>
                          <hr id="m_1830330970004194533zwchr">
                          <div><b>Kimden: </b>"Ali Nesin" <<a href="mailto:anesin@nesinkoyleri.org" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">anesin@nesinkoyleri.org</a>><br>
                            <b>Kime: </b>"Zafer ERCAN" <<a href="mailto:zercan@ibu.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">zercan@ibu.edu.tr</a>><br>
                            <b>Kk: </b>"Mustafa Polat" <<a href="mailto:mpolat@yeditepe.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">mpolat@yeditepe.edu.tr</a>>,
                            "yilmaz akyildiz" <<a href="mailto:yilmaz.akyildiz@gmail.com" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">yilmaz.akyildiz@gmail.com</a>>,
                            "turkmath" <<a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">turkmath@listweb.bilkent.edu.tr</a>>,
                            "tmd" <<a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">tmd-uye@listweb.bilkent.edu.tr</a>>,
                            "Ayşe Uyar" <<a href="mailto:ayseu@gazi.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">ayseu@gazi.edu.tr</a>>,
                            "Zafer ERCAN" <<a href="mailto:Zafer.Ercan@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">Zafer.Ercan@listweb.bilkent.edu.tr</a>><br>
                            <b>Gönderilenler: </b>29 Kasım Cuma 2024
                            14:22:20<br>
                            <b>Konu: </b>Re: [Turkmath:6800]
                            karadeniz aklı.. çalışmıyor 12 den sonra...
                            Ek i eklemeyi unutmuşum...<br>
                          </div>
                          <br>
                          <div>
                            <p><br>
                            </p>
                            <p>Söylediğin kitaptaki Proposition 3.14'e
                              şimdi baktım. Aynen söylediğimi söylüyor.
                              "Observation"a bak.<img src="cid:part1.5rSKxwXE.dUuD4iyX@metu.edu.tr" alt="" class=""></p>
                            <p>Bunu sabahın köründe, senin mesajını
                              almadan düşünmüştüm. İşte Whatsapp kanıtı:</p>
                            <p><img src="cid:part2.L6SFGCwd.2zT90709@metu.edu.tr" alt="" class=""></p>
                            <p>A<br>
                            </p>
                            <p><br>
                            </p>
                            <p><br>
                            </p>
                            <div>29.11.2024 12:48 tarihinde Zafer ERCAN
                              yazdı:<br>
                            </div>
                            <blockquote>
                              <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                                <div><br>
                                </div>
                                <div><br>
                                </div>
                                <div>Ali Nesin, numaralandırılmış
                                  açıklamalarını takip ederek yanıt
                                  vereceğim.</div>
                                <div><br>
                                </div>
                                <div>1. ''neyse diyelim'' sadakana
                                  ihtiyacım yok, sadakanı kendi cebine
                                  at!  İlgili yazımın birinci
                                  açıklamasına verdiğin yanıtı ekte
                                  ''seçim aksiyomu 1'' isimli </div>
                                <div>ekteki açıklamayı oku sonra gerekli
                                  mi gereksiz mi oyle karar ver,
                                  ukalalık ederek ya da hınç alma
                                  fırsatcılığıyla yanıt verme. ''henüz
                                  öğrenmiş'' de değilim, bu kadar açık
                                  bir konuda da</div>
                                <div>yanılıyorsun. İçime sindiremediğim
                                  konusunda haklısın.Öğrendiğimi
                                  zannettiğim her aşamada  tekrar
                                  sorguluyorum. Bu konuda seviyemi merak
                                  edersen online üzerinden konuşma </div>
                                <div>fırsatı oluşturabiliriz. Sizin
                                  5'te  biriniz kadar süreli bir
                                  konuşmaya hazırım. Muhattap olmam
                                  falan şımarıklığı falan çekme.</div>
                                <div><br>
                                </div>
                                <div>2. Demişin ki her bildiğini
                                  kanıtlamak zorunda mısın? Bir öenek
                                  ver! ve öncelikle  şunu söyle: Nereden
                                  bu kanıya vardın? Sen görüşlerine
                                  anlatınca  olunca paylaşım, hizmet şu
                                  bu. başakasının anlatımı olunca
                                  ''kanıtlamak zorunda mısın?'' demek
                                  zorunda mısın?<span style="font-size:12pt"> Haddini bil!
                                    Ayrıca ekteki seçim aksiyom 2
                                    başlıklı yazıyı oku. Burada seçim
                                    aksiyomunun denkliklerinin genel
                                    kardinaliteler üzerinden ilk akla
                                    gelen bir </span>anlama çabası
                                  olduğunu gör.. Ukalalık yapma.</div>
                                <div><br>
                                </div>
                                <div>3 Bu konuda Horst Herrlich'in axiom
                                  of choice adlı kitabın Teorem 3.14'e
                                  bakabilirsin.</div>
                                <div><br>
                                </div>
                                <div>Ali Nesin, kimin ne hizmet
                                  verdiğinin seviyesini belirleme
                                  şefliğinden kendini kurtar. Bir harf
                                  öğretenin kölesi olmayacağımız gibi
                                  matematik emekcisi Ali Nesin
                                  şeyhimizdir, diyecek de değiliz. </div>
                                <div><br>
                                </div>
                                <div>Kısmen konu dışı olacak ama
                                  bilinmesi gereken iki yüzlülüğünü
                                  yüzüne çarpmadan edemeyeceğim: Bir
                                  taraftan Aziz Nesin adına  verilen bir
                                  ödülü, ödülün verildiği alana giderek
                                  ve (Çiller ve benzerlerinin de
                                  ilgisini görmeyince de olsa) ''Tansu
                                  Çiller'e de verilen bir ödülü babam
                                  adına alamam'' diyerek sonuçta onurlu 
                                  bir davranışta bulundun, diğer
                                  taraftan sermayenin başçakalı
                                  Koçların  verdiği 100 bin dolar
                                  karşılığında Aziz Nesin ile Vehbi Koç 
                                  aynı yolun yolcusuydu diyecek kadar
                                  küçüldün. </div>
                                <div><br>
                                </div>
                                <div>Beni matematik köyü'nden kovma
                                  nedeninse,  sende hep bir dert olacak!</div>
                                <div><br>
                                </div>
                                <div>ZE </div>
                                <div><br>
                                </div>
                                <div><br>
                                </div>
                                <div><br>
                                </div>
                                <div><br>
                                </div>
                                <hr id="m_1830330970004194533zwchr">
                                <div><b>From: </b>"Ali Nesin" <a href="mailto:anesin@nesinkoyleri.org" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
                                    <anesin@nesinkoyleri.org></a><br>
                                  <b>To: </b>"Zafer ERCAN" <a href="mailto:zercan@ibu.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
                                    <zercan@ibu.edu.tr></a>,
                                  "Mustafa Polat" <a href="mailto:mpolat@yeditepe.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
                                    <mpolat@yeditepe.edu.tr></a><br>
                                  <b>Cc: </b>"yilmaz akyildiz" <a href="mailto:yilmaz.akyildiz@gmail.com" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
                                    <yilmaz.akyildiz@gmail.com></a>,
                                  "turkmath" <a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<turkmath@listweb.bilkent.edu.tr></a>, "tmd" <a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
                                    <tmd-uye@listweb.bilkent.edu.tr></a>,
                                  "Ayşe Uyar" <a href="mailto:ayseu@gazi.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
                                    <ayseu@gazi.edu.tr></a>,
                                  "Zafer ERCAN" <a href="mailto:Zafer.Ercan@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<Zafer.Ercan@listweb.bilkent.edu.tr></a><br>
                                  <b>Sent: </b>Friday, November 29,
                                  2024 1:56:30 AM<br>
                                  <b>Subject: </b>Re: [Turkmath:6800]
                                  karadeniz aklı.. çalışmıyor 12 den
                                  sonra... Ek i eklemeyi unutmuşum...<br>
                                </div>
                                <div><br>
                                </div>
                                <div>
                                  <p><br>
                                  </p>
                                  <p>Zafer Ercan'ın bu son mesajını pek
                                    dikkate almayın derim. <br>
                                  </p>
                                  <p>1) "Seçim aksiyomu sonlu kez
                                    uygulanarak ve bileşim aksiyomu
                                    kullanılarak küme ailesinin her
                                    elemanından sonlu eleman seçilerek
                                    ve onlardan oluşan bir küme elde
                                    edilebilir (yeterince eleman varsa
                                    elbet)." Bu kadar gereksiz bir
                                    cümleyi ancak Seçim Aksiyomu'nu
                                    henüz öğrenmiş ama yeterince
                                    sindirememiş bir öğrenci kurabilir.
                                    Neyse diyelim...<br>
                                  </p>
                                  <div>2) "Bir tane ya da sonlu tane
                                    eleman seçmek yerine küme ailesinin
                                    her elemanı seçilerek bunlardan
                                    oluşan bir küme elde edilebilir ki
                                    bu, bileşim aksiyomuna karşılık
                                    gelir. Eleman seçimini sonlulukla
                                    sınırlı tutulmadan belirli bir
                                    kardinalite de seçilen eleman
                                    üzerinden Seçim aksiyomuna denkimsi
                                    bağlantılar bulunabilir." Saçmalığın
                                    dik âlâsı! Bildiğin konulardan
                                    bahset Zafer, ukalalık yapma.
                                    Dediğin her şey yanlış değil, ama
                                    açıklaman saçma, hatta absürt! Hele
                                    ilk cümlen, kurtarılacak tarafı yok!
                                    Bu konuları çok iyi bildiğini
                                    kanıtlamaya mecbur musun? Ben pek
                                    bilmem doğrusu, ama saçmalığa da göz
                                    göre göre izin veremem!<br>
                                  </div>
                                  <div><br>
                                  </div>
                                  <div>3) "Seçim aksiyomunun kullanımına
                                    izin verildiğinde birçok kanıt çok
                                    daha kolay verilebilir, örneğin
                                    kapalı ve sinirli aralıkta tanımlı
                                    her sürekli fonksiyon düzgün
                                    süreklidir." Reellerin kapalı ve
                                    sınırlı aralıklarında tanımlanmış
                                    sürekli fonksiyonların düzgün
                                    sürekli olduklarının Seçim
                                    Aksiyomu'nu kullanmayan bir kanıtını
                                    doğrusu görmek isterim. Aşağıda
                                    Analiz IV kitabımdan bir kanıt var.
                                    O kanıtta her x_1 ve x_2 için bir y
                                    seçiliyor. Bu seçim Seçim Aksiyomu
                                    olmadan da yapılabilir gerçekten,
                                    y'yi x_1 ve x_2'nin orta noktasını
                                    almak yeterli olmalı. Peki Seçim
                                    Aksiyomu olmadan Lebegues sayısının
                                    varlığı nasıl kanıtlanıyor? İşte
                                    sana bildiğin bir konu. Bu konuda
                                    ahkam kes de bişeyler öğrenelim.<br>
                                  </div>
                                  <p><img src="cid:part3.hRXv0FEL.n0mHiO76@metu.edu.tr" alt="" class=""></p>
                                  <p>Ali<br>
                                  </p>
                                  <p><br>
                                  </p>
                                  <div>26.11.2024 21:29 tarihinde Zafer
                                    ERCAN yazdı:<br>
                                  </div>
                                  <blockquote>
                                    <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                                      <div>
                                        <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                                          <div>Seçim aksiyomunun belki
                                            de bilinen yüze yakın </div>
                                          <div>denki vardır. Bunların
                                            7-8 tanesi bu aksiyomun </div>
                                          <div>tanım formundadır. Seçim
                                            aksiyomunda esas olan eleman
                                            seçmek değil, belirli bir
                                            kuralla seçilmemiş serseri
                                            elemanların uyumlu
                                            yaşayacakları bir yuva
                                            bulmaktır.</div>
                                          <div><br>
                                          </div>
                                          <div>Seçim aksiyomu sonlu kez
                                            uygulanarak ve bileşim
                                            aksiyomu kullanılarak küme
                                            ailesinin her elemanından
                                            sonlu eleman seçilerek ve
                                            onlardan oluşan bir küme
                                            elde edilebilir (yeterince
                                            eleman varsa elbet).</div>
                                          <div><br>
                                          </div>
                                          <div>Bir tane ya da sonlu tane
                                            eleman seçmek yerine küme
                                            ailesinin her elemanı
                                            seçilerek bunlardan oluşan
                                            bir küme elde edilebilir ki
                                            bu, bileşim aksiyomuna
                                            karşılık gelir. Eleman
                                            seçimini sonlulukla sınırlı
                                            tutulmadan belirli bir
                                            kardinalite de seçilen
                                            eleman üzerinden Seçim
                                            aksiyomuna denkimsi
                                            bağlantılar bulunabilir.</div>
                                          <div><br>
                                          </div>
                                          <div>Seçim aksiyomunun
                                            kullanımına izin
                                            verildiğinde birçok kanıt
                                            çok daha kolay verilebilir,
                                            örneğin kapalı ve sinirli
                                            aralıkta tanımlı her sürekli
                                            fonksiyon düzgün süreklidir.</div>
                                          <div><br>
                                          </div>
                                          <div>Türkiye'de matematikçiler
                                            çok bilmişliklerinden dolayı
                                            Seçim aksiyomuyla kavga
                                            ediyorlar ama tutmuyor!</div>
                                          <div><br>
                                          </div>
                                          <div>Evet, lisansda Seçim
                                            aksiyomu öğretilmez (tamam
                                            tamam Ali Nesin
                                            öğretiyordu!) Ama farkına
                                            varmadan başka bir biçimde
                                            öğretilir.</div>
                                          <div><br>
                                          </div>
                                          <div><span style="font-size:12pt">Bu</span><span style="font-size:12pt">na
                                              karşın 85 milyondan oluşan
                                              Türkiye halkına Seçim
                                              aksiyomunu anlatacağım.</span><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>Tanrı Türkü Korusun.</div>
                                          <div><br>
                                          </div>
                                          <div>ZE</div>
                                          <div><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <hr id="m_1830330970004194533zwchr">
                                          <div><b>Kimden: </b>"Mustafa
                                            Polat" <a href="mailto:mpolat@yeditepe.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<mpolat@yeditepe.edu.tr></a><br>
                                            <b>Kime: </b>"yilmaz
                                            akyildiz" <a href="mailto:yilmaz.akyildiz@gmail.com" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<yilmaz.akyildiz@gmail.com></a><br>
                                            <b>Kk: </b>"turkmath" <a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<turkmath@listweb.bilkent.edu.tr></a>, "tmd" <a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<tmd-uye@listweb.bilkent.edu.tr></a>, "Ayşe Uyar" <a href="mailto:ayseu@gazi.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
                                              <ayseu@gazi.edu.tr></a>,
                                            "Zafer ERCAN" <a href="mailto:Zafer.Ercan@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<Zafer.Ercan@listweb.bilkent.edu.tr></a>, "Ali Nesin" <a href="mailto:anesin@nesinkoyleri.org" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">
<anesin@nesinkoyleri.org></a><br>
                                            <b>Gönderilenler: </b>26
                                            Kasım Salı 2024 7:33:37<br>
                                            <b>Konu: </b>Re: [Turkmath:6800]
                                            karadeniz aklı.. çalışmıyor
                                            12 den sonra... Ek i
                                            eklemeyi unutmuşum...<br>
                                          </div>
                                          <br>
                                          <div>
                                            <div dir="auto">Kasten
                                              değildi ama ZE nin topla
                                              münasebeti feci idi.</div>
                                            <div><br>
                                              <div class="gmail_quote">
                                                <div dir="ltr" class="gmail_attr">26
                                                  Kas 2024 Sal, saat
                                                  00:20 tarihinde yilmaz
                                                  akyildiz <<a href="mailto:yilmaz.akyildiz@gmail.com" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">yilmaz.akyildiz@gmail.com</a>>
                                                  şunu yazdı:<br>
                                                </div>
                                                <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb( 204 , 204 , 204 );padding-left:1ex">
                                                  <div dir="ltr">
                                                    <div class="gmail_quote">
                                                      <div dir="ltr" class="gmail_attr">On Mon, Nov 25, 2024 at 11:35 PM Mustafa Polat <<a href="mailto:mpolat@yeditepe.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">mpolat@yeditepe.edu.tr</a>>
                                                        wrote:<br>
                                                      </div>
                                                      <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb( 204 , 204 , 204 );padding-left:1ex">
                                                        <div dir="ltr">ZE
                                                          nin toplara
                                                          girişi
                                                          gerçekten
                                                          faullü. Bir
                                                          keresin Aydın
                                                          Aytuna yi
                                                          sakatlamıştı. </div>
                                                        <br>
                                                      </blockquote>
                                                      <div><span class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small"></span><span style="font-family:'verdana' , sans-serif">kasten yapmamıştır!</span></div>
                                                      <div dir="ltr">
                                                        <div class="gmail_default" style="font-family:'verdana' , sans-serif">ZE
                                                          nin işi
                                                          diliyle</div>
                                                        <div class="gmail_default" style="font-family:'verdana' , sans-serif">benim
                                                          ismime mesela
                                                          aldanmayın</div>
                                                        <div class="gmail_default" style="font-family:'verdana' , sans-serif">zafer
                                                          in de ben gibi
                                                          fizikman 
                                                          korkak
                                                          olduğundan
                                                          eminim.</div>
                                                        <div class="gmail_default" style="font-family:'verdana' , sans-serif">zaten
                                                          erkekliğin %98
                                                          i kaçmak değil
                                                          mi?</div>
                                                      </div>
                                                      <div><span style="font-family:'verdana' , sans-serif">erkek adam<span class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small">lar</span>dırız vesselam!</span> </div>
                                                    </div>
                                                  </div>
                                                  <div dir="ltr">
                                                    <div class="gmail_quote"><br>
                                                      <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb( 204 , 204 , 204 );padding-left:1ex">
                                                        <div class="gmail_quote">
                                                          <div dir="ltr" class="gmail_attr">On Mon, Nov 25, 2024 at 9:54 PM yilmaz akyildiz <<a href="mailto:yilmaz.akyildiz@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">yilmaz.akyildiz@listweb.bilkent.edu.tr</a>>
                                                          wrote:<br>
                                                          </div>
                                                          <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb( 204 , 204 , 204 );padding-left:1ex">
                                                          <div dir="ltr">
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Ek için link
                                                          vermekle
                                                          yetineceğim:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">ekmek için
                                                          ekmeleddin..</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><a href="https://drive.google.com/file/d/1mdsEXQ88Xt6Dk66YizkQn84ahzjFIlfg/view?usp=sharing" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">https://drive.google.com/file/d/1mdsEXQ88Xt6Dk66YizkQn84ahzjFIlfg/view?usp=sharing</a></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><br>
                                                          </div>
                                                          <div class="gmail_quote">
                                                          <div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>
                                                          <br>
                                                          </div>
                                                          <div dir="ltr" class="gmail_attr">Subject: ali ismini yazmamışmış, aziz nesin'in de
                                                          ismini yazması
                                                          gerekmiyordu..</div>
                                                          <div dir="ltr" class="gmail_attr"><span style="font-family:'verdana' , sans-serif"><br>
                                                          </span></div>
                                                          <div dir="ltr" class="gmail_attr"><span style="font-family:'verdana' , sans-serif">zaten
                                                          baba-oğul
                                                          dergileri
                                                          kendileri
                                                          çıkarıyorlardı.</span><br>
                                                          </div>
                                                          <div dir="ltr">
                                                          <div dir="ltr">
                                                          <div dir="auto">
                                                          <div dir="ltr">
                                                          <div dir="ltr">
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">bir de her
                                                          kapatıldığında
                                                          Baba Aziz yeni
                                                          bir adla
                                                          yoluna
                                                          yılmadan devam
                                                          etmiştir: </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><b><i>marko
                                                          paşa - malum
                                                          paşa - meçhul
                                                          paşa - öküz
                                                          paşa - bizim
                                                          paşa - merhum
                                                          paşa:</i></b></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><img src="cid:part4.S3PapEid.xoc0JchG@metu.edu.tr" alt="image.png" style="width:277px;max-width:100%" class=""><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Benim nesil <b><i>Akbaba</i></b>
                                                          ile büyüdü:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><img src="cid:part5.sCWqwgB3.3jw0KXws@metu.edu.tr" alt="image.png" style="width:600px;max-width:100%" class=""><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">gelelim ali
                                                          nesin' e:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">12 senede
                                                          törkiş
                                                          Bourbaki yi
                                                          yazdı:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><img src="cid:part6.gAgJzxNy.fD7c51gZ@metu.edu.tr" alt="image.png" style="width:760px;max-width:100%" class=""><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">şuna bizzat
                                                          şahidim:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">ilham kaynağı
                                                          matematik se
                                                          mazotu sek
                                                          rakı idi. </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Bira varsa
                                                          üstüne
                                                          cilasını da 
                                                          çekerdi.</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">(Bir ilham
                                                          kaynağı daha
                                                          var, zaten
                                                          onsuz
                                                          matematik
                                                          olmaz!)</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Atatürk de
                                                          sıhhatini
                                                          idealleri
                                                          için feda
                                                          etmiş birisidir.</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Baba Nesin in
                                                          ali'ye benim
                                                          bildiğim iki
                                                          nasihatı
                                                          vardı:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">1. matematik
                                                          köyü kur</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">2. bırak şu
                                                          zıkkımı, pek
                                                          çok kıymetli
                                                          dostumu ona
                                                          kurban verdim.</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Paul Erdöş de
                                                          Oxford
                                                          da verdiği son
                                                          konuşmasının
                                                          bir yerinde </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">birlikte
                                                          ispatladıkları
                                                          bir teoremden
                                                          bahsederken
                                                          bir an durup:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>"pek çok
                                                          dahi
                                                          meslektaşımı
                                                          ya nikotine ya
                                                          alkole ya da
                                                          intihara kurban
                                                          verdim"</i>
                                                          demişti.</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Arkadaşlar
                                                          şunu ben Aziz
                                                          Nesin'in
                                                          ağzından
                                                          bizzat duydum:</div>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>"hayatımın
                                                          sonuna
                                                          yaklaşırken en
                                                          büyük
                                                          pişmanlığım, </i></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>Atatürk'ü
                                                          çok geç
                                                          keşfetmiş
                                                          olmam dır..! </i></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>gözlerim
                                                          artık iyi
                                                          görmüyor.</i></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>onun
                                                          kitabını
                                                          yazmak çok
                                                          isterdim.</i></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>artık çok
                                                          geç".</i></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Bu konuşmayı
                                                          Aziz Baba
                                                          Boğaziçi
                                                          Üniversitesinde
                                                          o meşhur
                                                          salonda yaptı</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">ve en önde
                                                          oturanlar başı
                                                          bağlı kız
                                                          öğrencilerimizdi.</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">(Kaptan
                                                          Attila İlhan
                                                          da Divan
                                                          Pastanesinde
                                                          en çok
                                                          ziyaretine
                                                          gelenlerinin</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">başı bağlı
                                                          genç
                                                          kızlarımız
                                                          olduğunu
                                                          söylemişti.</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Böyle de
                                                          garip bir
                                                          ülkemiz var
                                                          bizim... başka
                                                          yerde ben
                                                          yaşayamam...)</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">ZE demiş ki:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>"<span style="color:rgb( 0 , 0 , 0 );font-family:'arial' , 'helvetica' , sans-serif;font-size:16px">Ali
                                                          Nesin imzalı
                                                          olarak  MD'nin
                                                          herhangi bir
                                                          sayısında 
                                                          Seçim beliti
                                                          ve Zorn önsavı
                                                          başlıklı bir
                                                          yazı yer
                                                          almamaktadır. </span></i><i><span style="color:rgb( 0 , 0 , 0 );font-family:'arial' , 'helvetica' , sans-serif;font-size:16px">Bunun
                                                          yanında 
                                                          imzasız
                                                          olarak </span></i><i style="font-size:16px;color:rgb( 0 , 0 , 0 );font-family:'arial' , 'helvetica' , sans-serif">2006-2
                                                          sayısında bu
                                                          başlıkta bir
                                                          yazı yer
                                                          almaktadır.<span class="gmail_default" style="font-family:'verdana' , sans-serif;font-size:small">" <b>(Ek)</b>.</span></i></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><br>
                                                          </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Yukarıda
                                                          demek
                                                          istediğim gibi
                                                          Matematik
                                                          Dünyasındaki o
                                                          isimsiz
                                                          yazıların
                                                          hepsini ali
                                                          nesin
                                                          yazmıştır.</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Bunu ZE de
                                                          bilir ama onun
                                                          derdi
                                                          başkadır.. </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Ayşe ile hoş
                                                          (ama içeriği
                                                          boş) vakit
                                                          geçirmek... </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Yahu şu
                                                          adamın gazını
                                                          almayı sadece
                                                          bana
                                                          bırakmayın!</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Siz de girin
                                                          topa..! </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Kaç defalar
                                                          duydum
                                                          bazılarınızdan
                                                          şu meyanda
                                                          sözler:</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><i>"ZE çok
                                                          defalar çok
                                                          haklı, ama
                                                          toplara girişi
                                                          faullü, direk
                                                          kırmızı
                                                          kart.."</i></div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">kalın
                                                          sağlıcakla</div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">y.a. </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><b>Ek</b>:
                                                          Matematik
                                                          Dünyası
                                                          2006-II den 40
                                                          sayfalık seçim
                                                          aksiyomu vbg
                                                          nin sadece ilk
                                                          3 sayfası. </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">Hiç bir
                                                          kitapta bu
                                                          konu bu derece
                                                          detaylı
                                                          yazılmamıştır. </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><b><i>Ayşe ve
                                                          Zafer' e e
                                                          özel
                                                          teşekkürlerimizle,</i></b> </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">saylerinde neler
                                                          öğrendik
                                                          neler.. </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small">iki çeler bir
                                                          meler... </div>
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"> </div>
                                                          <div class="gmail_quote">
                                                          <div dir="ltr" class="gmail_attr">On Sun, Nov 24, 2024 at 11:07 PM AYSE UYAR <<a href="mailto:ayseu@gazi.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">ayseu@gazi.edu.tr</a>>
                                                          wrote:<br>
                                                          </div>
                                                          <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb( 204 , 204 , 204 );padding-left:1ex">
                                                          <div>
                                                          <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                                                          <div>Zafer
                                                          Bey,</div>
                                                          <br>
                                                          <div>Yazı 2006
                                                          yılında
                                                          yayınlanmış
                                                          ise
                                                          haklısınız, o
                                                          yıllarda
                                                          yüksek lisans
                                                          öğrencisi
                                                          değil, post
                                                          doktora
                                                          araştırmacısı
                                                          idim. 2001
                                                          yılında
                                                          doktorayı
                                                          bitirdikten
                                                          sonra
                                                          (uygulanan
                                                          mobing
                                                          nedeniyle)
                                                          yıllarca
                                                          Araştırma
                                                          görevlisi
                                                          kadrosunda
                                                          kaldım.
                                                          Yardımcı
                                                          doçent
                                                          olduktan sonra
                                                          derslerimde
                                                          söz konusu
                                                          yazıdan (genel
                                                          olarak
                                                          derginin pek
                                                          çok
                                                          yazısından)
                                                          çok
                                                          faydalandığımdan,
                                                          söz konusu
                                                          yazıyı yüksek
                                                          lisans
                                                          öğrencisi
                                                          olduğum
                                                          yıllarda
                                                          okuduğumu
                                                          hatırlıyordum.
                                                          Hafızam beni
                                                          yanıltmış. Bu
                                                          önemli (!)
                                                          düzeltme için
                                                          teşekkür
                                                          ederim.
                                                          Özgeçmişimi bu
                                                          kadar yakından
                                                          bilmeniz de
                                                          takdire şayan
                                                          doğrusu.  <br>
                                                           </div>
                                                          <div>Selamlar<br>
                                                          <br>
                                                          Ayşe Uyar</div>
                                                          <br>
                                                          <hr id="m_1830330970004194533m_-3609279668718265215m_1984891622991977872m_3903320645998433877m_-8413057745579822377m_7584278301376894179m_7121925290864780885m_5537403362483830147m_-3363868583342690764zwchr">
                                                          <div><b>Kimden:
                                                          </b>"Zafer
                                                          ERCAN" <<a href="mailto:zercan@ibu.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">zercan@ibu.edu.tr</a>><br>
                                                          <b>Kime: </b>"Ayşe
                                                          Uyar" <<a href="mailto:ayseu@gazi.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">ayseu@gazi.edu.tr</a>><br>
                                                          <b>Kk: </b>"yilmaz
                                                          akyildiz" <<a href="mailto:yilmaz.akyildiz@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">yilmaz.akyildiz@listweb.bilkent.edu.tr</a>>,
                                                          "tmd" <<a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">tmd-uye@listweb.bilkent.edu.tr</a>>,
                                                          "turkmath"
                                                          <<a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">turkmath@listweb.bilkent.edu.tr</a>>,
                                                          "Ali Nesin"
                                                          <<a href="mailto:anesin@nesinkoyleri.org" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">anesin@nesinkoyleri.org</a>><br>
                                                          <b>Gönderilenler:
                                                          </b>24 Kasım
                                                          Pazar 2024
                                                          22:11:24<br>
                                                          <b>Konu: </b>Re:
                                                          [TMD-UYE:
                                                          4201] Re: Ali
                                                          Nesin den
                                                          tekmili
                                                          birden: Seçim
                                                          Aksiyomu
                                                          Üzerine 13
                                                          ders<br>
                                                          </div>
                                                          <br>
                                                          <div>
                                                          <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                                                          <br>
                                                          <div>Ayşe
                                                          hanım,</div>
                                                          <br>
                                                          <div>Ali Nesin
                                                          imzalı olarak 
                                                          MD'nin
                                                          herhangi bir
                                                          sayısında 
                                                          Seçim beliti
                                                          ve Zorn önsavı
                                                          başlıklı bir
                                                          yazı
                                                          almamaktadır.
                                                          Bunun yanında 
                                                          imzasız
                                                          olarak </div>
                                                          <div>2006-2
                                                          sayısında bu
                                                          başlıkta bir
                                                          yazı yer
                                                          almaktadır.
                                                          Tahminim
                                                          bahsettiğiniz
                                                          yazı bu
                                                          olmasına
                                                          karşın, sizin
                                                          öğrenciliğiniz
                                                          bu tarihten 14
                                                          yıl önce </div>
                                                          <div>sona
                                                          ermiş
                                                          olduğundan söz
                                                          konusu yazıyı
                                                          okumuş olsanız
                                                          bile öğrenci
                                                          iken okumuş
                                                          olmanız söz
                                                          konusu
                                                          olamaz..</div>
                                                          <br>
                                                          <div>Saygılarımla.</div>
                                                          <br>
                                                          <div>Zafer
                                                          Ercan</div>
                                                          <br>
                                                          <hr id="m_1830330970004194533m_-3609279668718265215m_1984891622991977872m_3903320645998433877m_-8413057745579822377m_7584278301376894179m_7121925290864780885m_5537403362483830147m_-3363868583342690764zwchr">
                                                          <div><b>From:
                                                          </b>"Ayşe
                                                          Uyar" <<a href="mailto:ayseu@gazi.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">ayseu@gazi.edu.tr</a>><br>
                                                          <b>To: </b>"yilmaz
                                                          akyildiz" <<a href="mailto:yilmaz.akyildiz@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">yilmaz.akyildiz@listweb.bilkent.edu.tr</a>><br>
                                                          <b>Cc: </b>"tmd"
                                                          <<a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">tmd-uye@listweb.bilkent.edu.tr</a>>,
                                                          "turkmath"
                                                          <<a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">turkmath@listweb.bilkent.edu.tr</a>>,
                                                          "Ali Nesin"
                                                          <<a href="mailto:anesin@nesinkoyleri.org" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">anesin@nesinkoyleri.org</a>><br>
                                                          <b>Sent: </b>Saturday,
                                                          November 23,
                                                          2024 9:00:45
                                                          PM<br>
                                                          <b>Subject: </b>[TMD-UYE:
                                                          4201] Re: Ali
                                                          Nesin den
                                                          tekmili
                                                          birden: Seçim
                                                          Aksiyomu
                                                          Üzerine 13
                                                          ders<br>
                                                          </div>
                                                          <br>
                                                          <div>
                                                          <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                                                          <div>Matematik
                                                          dünyası
                                                          dergisinde Ali
                                                          Nesin'in Seçim
                                                          beliti ve Zorn
                                                          önsavı üzerine
                                                          bir yazısı
                                                          var. Henüz
                                                          öğrenci iken
                                                          okumuştum.
                                                          Dergiler
                                                          yanımda
                                                          olmadığından,
                                                          hangi sayı
                                                          olduğunu
                                                          bulamadım.
                                                          Yılmaz hocanın
                                                          paylaştığı
                                                          linkte de çok
                                                          güzel videolar
                                                          var ama  o
                                                          sayıyı merak
                                                          ettim.
                                                          Bilenler
                                                          listeye
                                                          yazarsa memnun
                                                          olurum. <br>
                                                          <br>
                                                          Aslında her
                                                          şey dijital
                                                          ortamda artık.
                                                          Matematik
                                                          dünyası
                                                          dergisi de
                                                          e-dergi
                                                          çıkarıp,
                                                          e-abonelik
                                                          sistemiyle
                                                          çalışsa güzel
                                                          olur diye
                                                          düşünüyorum.
                                                          İsteyen yine
                                                          dergi
                                                          biçiminde
                                                          alabilir. Öte
                                                          yandan benim
                                                          gibi pdf
                                                          üzerinden
                                                          okumayı
                                                          severlerin çok
                                                          işine
                                                          yarayacaktır.
                                                          Yüzlerce
                                                          kitabı,
                                                          makaleyi
                                                          tablete
                                                          indirip dağda
                                                          bayırda
                                                          okuyabilmek,
                                                          sanırım bu
                                                          çağdaki en
                                                          önemli
                                                          şansımız.
                                                          Teknolojik
                                                          imkanların
                                                          dışında başka
                                                          da kayda değer
                                                          bir şeylerin
                                                          olduğu bir
                                                          çağda
                                                          yaşamıyoruz
                                                          maalesef.  <br>
                                                          <br>
                                                          Son olarak, bu
                                                          listenin bir
                                                          de facebook
                                                          grubu
                                                          oluşturulsa
                                                          güzel olur
                                                          diye
                                                          düşünüyorum.
                                                          Pek çok açıdan
                                                          daha
                                                          kullanışlı bir
                                                          ortam. <br>
                                                          <br>
                                                          </div>
                                                          <div>Selamlar </div>
                                                          <br>
                                                          <div>Ayşe Uyar</div>
                                                          <hr id="m_1830330970004194533m_-3609279668718265215m_1984891622991977872m_3903320645998433877m_-8413057745579822377m_7584278301376894179m_7121925290864780885m_5537403362483830147m_-3363868583342690764zwchr">
                                                          <div><b>Kimden:
                                                          </b>"yilmaz
                                                          akyildiz" <<a href="mailto:yilmaz.akyildiz@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">yilmaz.akyildiz@listweb.bilkent.edu.tr</a>><br>
                                                          <b>Kime: </b>"turkmath"
                                                          <<a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">turkmath@listweb.bilkent.edu.tr</a>>,
                                                          "tmd" <<a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">tmd-uye@listweb.bilkent.edu.tr</a>><br>
                                                          <b>Kk: </b>"Ali
                                                          Nesin" <<a href="mailto:anesin@nesinkoyleri.org" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">anesin@nesinkoyleri.org</a>><br>
                                                          <b>Gönderilenler:
                                                          </b>23 Kasım
                                                          Cumartesi 2024
                                                          20:35:23<br>
                                                          <b>Konu: </b>[TMD-UYE:
4200]        Ali Nesin den tekmili birden: Seçim Aksiyomu Üzerine 13
                                                          ders<br>
                                                          </div>
                                                          <br>
                                                          <div>
                                                          <div dir="ltr">
                                                          <div dir="ltr">
                                                          <div style="font-family:'verdana' , sans-serif;font-size:small"><a href="https://www.youtube.com/c/NesinMatematikK%C3%B6y%C3%BCResmi/search?query=se%C3%A7im" style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">https://www.youtube.com/c/NesinMatematikK%C3%B6y%C3%BCResmi/search?query=se%C3%A7im</a></div>
                                                          <div class="gmail_quote">
                                                          <div>
                                                          <div style="font-family:'arial' , 'helvetica' , sans-serif;font-size:12pt;color:rgb( 0 , 0 , 0 )">
                                                          <div class="gmail_quote">
                                                          <div> </div>
                                                          <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb( 204 , 204 , 204 );padding-left:1ex">
                                                          > On
                                                          22-11-2024
                                                          03:43, Ali
                                                          Nesin wrote:<br>
                                                          <br>
                                                          > 1) Seçim
                                                          Aksiyomu
                                                          düzgün bir
                                                          lisans
                                                          eğitiminde
                                                          bilinmesi
                                                          gerekir. Ama<br>
                                                          > biraz
                                                          fazla uçuk
                                                          geldiği için
                                                          pek
                                                          önemsenmez. En
                                                          azından benim
                                                          deneyimim bu<br>
                                                          > yönde.<br>
                                                          ><br>
                                                          > 2) Zorn
                                                          Önsavı Seçim
                                                          Aksiyomu'ndan
                                                          çok daha
                                                          işlevseldir,
                                                          özellikle<br>
                                                          > cebirde.
                                                          Ya da şöyle
                                                          diyeyim, Seçim
                                                          Aksiyomu
                                                          kullanılan
                                                          yerler lisans<br>
                                                          >
                                                          öğrencileri
                                                          tarafından pek
                                                          önemsenmez,
                                                          ama Zorn
                                                          Önsavı
                                                          gerçekten her
                                                          zaman<br>
                                                          > çok
                                                          şaşırtıcı
                                                          sonuçlar
                                                          verir. Bir
                                                          başka deyişle:
                                                          Seçim Aksiyomu
                                                          farkına<br>
                                                          > varmadan
                                                          kullanılabilir
                                                          (okura
                                                          yutturabilirsin),
                                                          ama Zorn
                                                          Önsavı'nı
                                                          farkına<br>
                                                          > varmadan
                                                          kullanmak
                                                          imkânsızdır.<br>
                                                          ><br>
                                                          > 3) Oysa
                                                          Zorn
                                                          Önsavı'yla
                                                          Seçim Aksiyomu
                                                          (bilindiği
                                                          üzere)
                                                          birbirine<br>
                                                          > denktir.
                                                          İyi bir lisans
                                                          öğrencisi
                                                          kanıtını
                                                          bilmese de
                                                          bunu bilmeli.<br>
                                                          ><br>
                                                          > 4)
                                                          Analizde Seçim
                                                          Aksiyomu,
                                                          sağda solda,
                                                          orada burada
                                                          hemen hiç<br>
                                                          >
                                                          bahsedilmeden
                                                          kullanılır.
                                                          Arada bir bu
                                                          hoyratlık
                                                          cebirde de
                                                          yapılır, ama<br>
                                                          > çok daha
                                                          enderdir.
                                                          Genel olarak
                                                          analizciler
                                                          Seçim
                                                          Aksiyomu'nu
                                                          hiç<br>
                                                          >
                                                          sorgulamadan
                                                          kabul ederler.
                                                          Ayşe Uyar'ın
                                                          verdiği örnek
                                                          buna güzel bir<br>
                                                          > örnektir:
                                                          eşmerkezli ve
                                                          1/n yarıçaplı
                                                          her yuvardan
                                                          bir eleman
                                                          seçmek tabii<br>
                                                          > ki Seçim
                                                          Aksiyomu'yla
                                                          mümkündür ama
                                                          analizciler
                                                          bunu (haklı
                                                          olarak
                                                          aslında)<br>
                                                          > pek
                                                          önemsemezler.
                                                          Öte yandan
                                                          cebirde mesela
                                                          maksimal
                                                          idealin
                                                          varlığını<br>
                                                          >
                                                          kanıtlamak
                                                          için Zorn
                                                          Önsavı'nı
                                                          öğrencilerin
                                                          gözüne sokmak
                                                          zorundasın,
                                                          yoksa<br>
                                                          > ayaklanıp
                                                          isyan ederler.<br>
                                                          ><br>
                                                          > 5) Bilgi
Üniversitesi'nde bütün bunları tüm ayrıntılarıyla birinci sınıf<br>
                                                          >
                                                          öğrencilerime
anlatıyordum/anlatıorduk. Felsefesiyle tabii ki. Bana ve bize<br>
                                                          >
                                                          benzemelerini
istemiyordum/istemiyorduk! Ne yazık ki 26 yıl süren Bilgi<br>
                                                          > efsanesi
                                                          sona erdi.
                                                          Şimdi benzer
                                                          bir yapıyı
                                                          korsan olarak
                                                          Matematik<br>
                                                          > Köyü'nde
                                                          kurmaya
                                                          çalışıyorum.<br>
                                                          ><br>
                                                          > 6) Son
                                                          olarak bir
                                                          (A_i)_{i \in
                                                          I} küme
                                                          ailesinin
                                                          matematiksel
                                                          tanımını<br>
                                                          > vereyim.
                                                          I ve X birer
                                                          küme olsun.
                                                          I'dan X'e
                                                          giden bir f
                                                          fonksiyonuna
                                                          küme<br>
                                                          > ailesi
                                                          denir! Bu
                                                          kadar basit!
                                                          Eğer i \in I
                                                          için f(i) =
                                                          A_i ise, (X'i
                                                          yok<br>
                                                          > sayıp!)
                                                          bu fonksiyonu
                                                          (A_i)_{i \in
                                                          I} olarak
                                                          yazarız.<br>
                                                          ><br>
                                                          > Ali<br>
                                                          </blockquote>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          <br>
_______________________________________________<br>
                                                          Bu e-postayı
                                                          Türk Matematik
                                                          Derneği'nin
                                                          TMD-UYE
                                                          E-Posta
                                                          Listesine üye
                                                          olduğunuz için
                                                          aldınız.<br>
                                                          <a href="mailto:TMD-UYE@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">TMD-UYE@listweb.bilkent.edu.tr</a><br>
                                                          BU E-POSTA
                                                          LİSTEDEN
                                                          ÇIKMAK
                                                          (UNSUBSCRIBE)
                                                          VEYA ÜYELİK
                                                          SEÇENEKLERİNİ
                                                          DÜZENLEMEK
                                                          İÇİN aşağıda
                                                          bağlantısı
                                                          verilen
                                                          sayfayı
                                                          ziyaret
                                                          ediniz:<br>
                                                          <a href="http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye</a><br>
                                                          </div>
                                                          </div>
                                                          <br>
                                                          --<br>
                                                          <p>Bu e-posta
                                                          mesajı ve
                                                          içeriği gizli
                                                          veya özel
                                                          bilgiler
                                                          içerebilir.
                                                          Mesajın
                                                          içeriğinde
                                                          bulunan tüm
                                                          fikir ve
                                                          görüşler
                                                          sadece
                                                          göndericiye
                                                          ait olup, Gazi
Üniversitesi’nin resmi görüşünü yansıtmaz. Kurumumuz bu e-posta
                                                          içeriğindeki
                                                          bilgilerin
                                                          kullanılması
                                                          nedeniyle hiç
                                                          kimseye karşı
                                                          sorumlu
                                                          tutulamaz.
                                                          Mesajın
                                                          belirlenen
                                                          alıcılardan
                                                          biri
                                                          değilseniz,
                                                          mesaj
                                                          içeriğini ya
                                                          da eklerini
                                                          kullanmayınız,
kopyalamayınız, yaymayınız, başka kişilere yönlendirmeyiniz ve mesajı
                                                          gönderen
                                                          kişiyi derhal
                                                          e-posta
                                                          yoluyla
                                                          haberdar
                                                          ederek bu
                                                          mesajı ve
                                                          eklerini
                                                          herhangi bir
                                                          kopyasını
                                                          muhafaza
                                                          etmeksizin
                                                          siliniz.
                                                          Kurumumuz
                                                          size, mesajın
                                                          ve
                                                          bilgilerinin
                                                          değişikliğe
                                                          uğramaması,
                                                          bütünlüğünün
                                                          ve gizliliğin
                                                          korunması
                                                          konusunda
                                                          garanti
                                                          vermemekte
                                                          olup, e-posta
                                                          içeriğine
                                                          yetkisiz
                                                          olarak yapılan
                                                          müdahale,
                                                          virüs içermesi
                                                          ve/veya
                                                          bilgisayar
                                                          sisteminize
                                                          verebileceği
                                                          herhangi bir
                                                          zarardan da
                                                          sorumlu
                                                          değildir.</p>
                                                          <hr>
                                                          <p>This e-mail
                                                          message and
                                                          its content
                                                          may contain
                                                          confidential
                                                          or proprietary
                                                          information.
                                                          All ideas and
                                                          opinions
                                                          contained in
                                                          the message
                                                          are solely
                                                          those of the
                                                          sender and do
                                                          not reflect
                                                          the official
                                                          opinion of
                                                          Gazi
                                                          University.
                                                          Our
                                                          institution
                                                          cannot be held
                                                          responsible to
                                                          anyone for the
                                                          use of the
                                                          information
                                                          contained in
                                                          this e-mail.
                                                          If you are not
                                                          one of the
                                                          designated
                                                          recipients of
                                                          the message,
                                                          do not use,
                                                          copy,
                                                          disseminate,
                                                          forward the
                                                          message
                                                          content or
                                                          attachments,
                                                          and
                                                          immediately
                                                          notify the
                                                          sender of the
                                                          message via
                                                          e-mail and
                                                          delete this
                                                          message and
                                                          its
                                                          attachments
                                                          without
                                                          retaining any
                                                          copies. Our
                                                          institution
                                                          does not
                                                          guarantee you
                                                          that the
                                                          message and
                                                          its
                                                          information
                                                          will not be
                                                          changed, its
                                                          integrity and
confidentiality will be protected, and is not responsible for any
                                                          unauthorized
                                                          intervention
                                                          to the e-mail
                                                          content,
                                                          viruses and/or
                                                          any damage it
                                                          may cause to
                                                          your computer
                                                          system.</p>
                                                          <br>
_______________________________________________<br>
                                                          Bu e-postayı
                                                          Türk Matematik
                                                          Derneği'nin
                                                          TMD-UYE
                                                          E-Posta
                                                          Listesine üye
                                                          olduğunuz için
                                                          aldınız.<br>
                                                          <a href="mailto:TMD-UYE@listweb.bilkent.edu.tr" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">TMD-UYE@listweb.bilkent.edu.tr</a><br>
                                                          BU E-POSTA
                                                          LİSTEDEN
                                                          ÇIKMAK
                                                          (UNSUBSCRIBE)
                                                          VEYA ÜYELİK
                                                          SEÇENEKLERİNİ
                                                          DÜZENLEMEK
                                                          İÇİN aşağıda
                                                          bağlantısı
                                                          verilen
                                                          sayfayı
                                                          ziyaret
                                                          ediniz:<br>
                                                          <a href="http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye</a></div>
                                                          </div>
                                                          <br>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
_______________________________________________<br>
                                                          Turkmath
                                                          mailing list<br>
                                                          <a href="mailto:Turkmath@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">Turkmath@listweb.bilkent.edu.tr</a><br>
                                                          <a href="http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/turkmath" rel="noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/turkmath</a><br>
                                                          </blockquote>
                                                        </div>
                                                      </blockquote>
                                                    </div>
                                                  </div>
                                                </blockquote>
                                              </div>
                                            </div>
                                          </div>
                                        </div>
                                        <br>
                                      </div>
                                    </div>
                                  </blockquote>
                                  <div id="m_1830330970004194533DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br>
                                    <table style="border-top:1px solid rgb( 211 , 212 , 222 )"><tbody><tr><td style="width:55px;padding-top:13px"><a href="https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank"><img alt="" width="46" height="29" style="width:46px;height:29px" src="https://s-install.avcdn.net/ipm/preview/icons/icon-envelope-tick-round-orange-animated-no-repeat-v1.gif"></a></td><td style="width:470px;padding-top:12px;color:rgb( 65 , 66 , 78 );font-size:13px;font-family:'arial' , 'helvetica' , sans-serif;line-height:18px">
                                            Virüs yok.<a href="https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" style="color:rgb( 68 , 83 , 234 )" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer" target="_blank">www.avast.com</a></td></tr></tbody></table>
                                  </div>
                                  <br>
                                </div>
                              </div>
                            </blockquote>
                            <br>
                          </div>
                        </div>
                        <br>
                        --<br>
                        <p>Bu e-posta mesajı ve içeriği gizli veya özel
                          bilgiler içerebilir. Mesajın içeriğinde
                          bulunan tüm fikir ve görüşler sadece
                          göndericiye ait olup, Gazi Üniversitesi’nin
                          resmi görüşünü yansıtmaz. Kurumumuz bu e-posta
                          içeriğindeki bilgilerin kullanılması nedeniyle
                          hiç kimseye karşı sorumlu tutulamaz. Mesajın
                          belirlenen alıcılardan biri değilseniz, mesaj
                          içeriğini ya da eklerini kullanmayınız,
                          kopyalamayınız, yaymayınız, başka kişilere
                          yönlendirmeyiniz ve mesajı gönderen kişiyi
                          derhal e-posta yoluyla haberdar ederek bu
                          mesajı ve eklerini herhangi bir kopyasını
                          muhafaza etmeksizin siliniz. Kurumumuz size,
                          mesajın ve bilgilerinin değişikliğe
                          uğramaması, bütünlüğünün ve gizliliğin
                          korunması konusunda garanti vermemekte olup,
                          e-posta içeriğine yetkisiz olarak yapılan
                          müdahale, virüs içermesi ve/veya bilgisayar
                          sisteminize verebileceği herhangi bir zarardan
                          da sorumlu değildir.</p>
                        <hr>
                        <p>This e-mail message and its content may
                          contain confidential or proprietary
                          information. All ideas and opinions contained
                          in the message are solely those of the sender
                          and do not reflect the official opinion of
                          Gazi University. Our institution cannot be
                          held responsible to anyone for the use of the
                          information contained in this e-mail. If you
                          are not one of the designated recipients of
                          the message, do not use, copy, disseminate,
                          forward the message content or attachments,
                          and immediately notify the sender of the
                          message via e-mail and delete this message and
                          its attachments without retaining any copies.
                          Our institution does not guarantee you that
                          the message and its information will not be
                          changed, its integrity and confidentiality
                          will be protected, and is not responsible for
                          any unauthorized intervention to the e-mail
                          content, viruses and/or any damage it may
                          cause to your computer system.</p>
                      </div>
                    </div>
                  </div>
                </blockquote>
              </div>
              <br>
            </div>
          </div>
          <br>
          <fieldset class="moz-mime-attachment-header"></fieldset>
          <pre class="moz-quote-pre">_______________________________________________
Bu e-postayı Türk Matematik Derneği'nin TMD-UYE E-Posta Listesine üye olduğunuz için aldınız.
<a href="mailto:TMD-UYE@listweb.bilkent.edu.tr" target="_blank" rel="nofollow noopener noreferrer">TMD-UYE@listweb.bilkent.edu.tr</a>
BU E-POSTA LİSTEDEN ÇIKMAK (UNSUBSCRIBE) VEYA ÜYELİK SEÇENEKLERİNİ DÜZENLEMEK İÇİN aşağıda bağlantısı verilen sayfayı ziyaret ediniz:
<a href="http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye" target="_blank" rel="nofollow noopener noreferrer">http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye</a>
</pre>
        </blockquote>
        <p><strong> </strong></p>
        <table style="height:5px;width:760px"><tbody><tr style="height:6px"><td style="width:85px;text-align:center;height:6px"><span style="font-size:11px;background-color:red;color:white">[Harici
                  E-Posta] </span></td><td style="font-size:11px;width:660px;height:6px">Göndereni
                tanımıyorsanız ve içeriğin güvenli olduğundan emin
                değilseniz, <strong>lütfen linke tıklamayınız ve ekleri
                  açmayınız<em style="font-size:2px;color:black">iii</em></strong></td></tr><tr style="height:6px"><td style="width:85px;text-align:center;height:6px"><span style="font-size:11px;background-color:red;color:white">[External
                  E-Mail] </span></td><td style="font-size:11px;width:660px;height:6px">If
                you don't know the sender and you are not sure that the
                content is safe, <strong>please do not click on the
                  link and do not open attachments.</strong></td></tr></tbody></table>
        <p><br>
          <br>
        </p>
        <br>
        <fieldset class="moz-mime-attachment-header"></fieldset>
        <pre class="moz-quote-pre">_______________________________________________
Bu e-postayı Türk Matematik Derneği'nin TMD-UYE E-Posta Listesine üye olduğunuz için aldınız.
<a href="mailto:TMD-UYE@listweb.bilkent.edu.tr" target="_blank" rel="nofollow noopener noreferrer">TMD-UYE@listweb.bilkent.edu.tr</a>
BU E-POSTA LİSTEDEN ÇIKMAK (UNSUBSCRIBE) VEYA ÜYELİK SEÇENEKLERİNİ DÜZENLEMEK İÇİN aşağıda bağlantısı verilen sayfayı ziyaret ediniz:
<a href="http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye" target="_blank" rel="nofollow noopener noreferrer">http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye</a>
</pre>
      </blockquote>
    </blockquote>
  <br>_______________________________________________<br>Bu e-postayı Türk Matematik Derneği'nin TMD-UYE E-Posta Listesine üye olduğunuz için aldınız.<br>TMD-UYE@listweb.bilkent.edu.tr<br>BU E-POSTA LİSTEDEN ÇIKMAK (UNSUBSCRIBE) VEYA ÜYELİK SEÇENEKLERİNİ DÜZENLEMEK İÇİN aşağıda bağlantısı verilen sayfayı ziyaret ediniz:<br>http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/tmd-uye<br></div></div></body></html>