<div dir="auto"><div>Neden ki? <div dir="auto"><br></div><div dir="auto">Bu arada, madem ki perfect square,  2025 için nasıl unuturuz şunu:  </div><div dir="auto"><br></div><div dir="auto">1+3+5+...+(2n-1)=n^{2}.  n=45 ==> n^{2}=45^{2}=2025. </div><div dir="auto">Yani:  </div><div dir="auto">1+3+5+7+...+89=2025.</div><div dir="auto"><br></div><div dir="auto">Hiç umudum yok ama, </div><div dir="auto">İnsanlık için iyi bir yıl olsun dileklerimle.</div><br><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">1 Oca 2025 Çar 23:40 tarihinde Ali Nesin <<a href="mailto:anesin@nesinkoyleri.org">anesin@nesinkoyleri.org</a>> şunu yazdı:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><u></u>

  
    
  
  <div>
    <p><br>
    </p>
    <p>1) Fermat'nın Son Teoremi'nin kanıtında Seçim Aksiyomu
      kullanıldığına inanmak istemiyorum. <br>
      2) Kullanıldıysa da gereksiz yere, kanıtı kısaltmak için
      umursamadan, dikkatsizce kullanılmıştır.<br>
      3) Eğer kanıtta Seçim Aksiyomu'nu kullanmak illa gerekliyse, Seçim
      Aksiyomu kullanılmadan da bir kanıtı vardır. Felsefe söyletiyor.<br>
      4) Eğer öyle bir şey olsaydı, eminim bugün birçok matematikçi
      Fermat'nın Son Teoremi'ni Seçim Aksiyomu kullanmadan kanıtlamaya
      çalışırdı ve böyle bir uğraştan hepimizin haberi olurdu.<br>
      A<br>
    </p>
    <p><br>
    </p>
    <div>02.12.2024 14:25 tarihinde Zafer ERCAN
      yazdı:<br>
    </div>
    <blockquote type="cite">
      
      <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="m_-726137518740113417zwchr">
        <div><b>From: </b>"yilmaz akyildiz"
          <a href="mailto:yilmaz.akyildiz@gmail.com" target="_blank" rel="noreferrer"><yilmaz.akyildiz@gmail.com></a><br>
          <b>To: </b>"Zafer ERCAN" <a href="mailto:zercan@ibu.edu.tr" target="_blank" rel="noreferrer"><zercan@ibu.edu.tr></a><br>
          <b>Cc: </b>"Ayşe Uyar" <a href="mailto:ayseu@gazi.edu.tr" target="_blank" rel="noreferrer"><ayseu@gazi.edu.tr></a>, "Ali Nesin"
          <a href="mailto:anesin@nesinkoyleri.org" target="_blank" rel="noreferrer"><anesin@nesinkoyleri.org></a>, "Mustafa Polat"
          <a href="mailto:mpolat@yeditepe.edu.tr" target="_blank" rel="noreferrer"><mpolat@yeditepe.edu.tr></a>, "turkmath"
          <a href="mailto:turkmath@listweb.bilkent.edu.tr" target="_blank" rel="noreferrer"><turkmath@listweb.bilkent.edu.tr></a>, "tmd"
          <a href="mailto:tmd-uye@listweb.bilkent.edu.tr" target="_blank" rel="noreferrer"><tmd-uye@listweb.bilkent.edu.tr></a>, "Zafer ERCAN"
          <a href="mailto:Zafer.Ercan@listweb.bilkent.edu.tr" target="_blank" rel="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">
            <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 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_-726137518740113417m_1830330970004194533zwchr">
                  <div><b>From: </b>"Ayşe Uyar" <<a href="mailto:ayseu@gazi.edu.tr" rel="nofollow noopener noreferrer noreferrer" target="_blank">ayseu@gazi.edu.tr</a>><br>
                    <b>To: </b>"Ali Nesin" <<a href="mailto:anesin@nesinkoyleri.org" rel="nofollow noopener noreferrer noreferrer" target="_blank">anesin@nesinkoyleri.org</a>><br>
                    <b>Cc: </b>"Zafer ERCAN" <<a href="mailto:zercan@ibu.edu.tr" rel="nofollow noopener noreferrer noreferrer" target="_blank">zercan@ibu.edu.tr</a>>,
                    "Mustafa Polat" <<a href="mailto:mpolat@yeditepe.edu.tr" rel="nofollow noopener noreferrer noreferrer" target="_blank">mpolat@yeditepe.edu.tr</a>>,
                    "yilmaz akyildiz" <<a href="mailto:yilmaz.akyildiz@gmail.com" rel="nofollow noopener noreferrer noreferrer" target="_blank">yilmaz.akyildiz@gmail.com</a>>,
                    "turkmath" <<a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer noreferrer" target="_blank">turkmath@listweb.bilkent.edu.tr</a>>,
                    "tmd" <<a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer 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 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_-726137518740113417m_1830330970004194533zwchr">
                      <div><b>Kimden: </b>"Ali Nesin" <<a href="mailto:anesin@nesinkoyleri.org" rel="nofollow noopener noreferrer noreferrer" target="_blank">anesin@nesinkoyleri.org</a>><br>
                        <b>Kime: </b>"Zafer ERCAN" <<a href="mailto:zercan@ibu.edu.tr" rel="nofollow noopener noreferrer 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 noreferrer" target="_blank">mpolat@yeditepe.edu.tr</a>>,
                        "yilmaz akyildiz" <<a href="mailto:yilmaz.akyildiz@gmail.com" rel="nofollow noopener noreferrer noreferrer" target="_blank">yilmaz.akyildiz@gmail.com</a>>,
                        "turkmath" <<a href="mailto:turkmath@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer noreferrer" target="_blank">turkmath@listweb.bilkent.edu.tr</a>>,
                        "tmd" <<a href="mailto:tmd-uye@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer noreferrer" target="_blank">tmd-uye@listweb.bilkent.edu.tr</a>>,
                        "Ayşe Uyar" <<a href="mailto:ayseu@gazi.edu.tr" rel="nofollow noopener noreferrer noreferrer" target="_blank">ayseu@gazi.edu.tr</a>>,
                        "Zafer ERCAN" <<a href="mailto:Zafer.Ercan@listweb.bilkent.edu.tr" rel="nofollow noopener noreferrer 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:ii_19423d67e905b2f6de01" alt=""></p>
                        <p>Bunu sabahın köründe, senin mesajını almadan
                          düşünmüştüm. İşte Whatsapp kanıtı:</p>
                        <p><img src="cid:ii_19423d67e91654f1abd2" alt=""></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_-726137518740113417m_1830330970004194533zwchr">
                            <div><b>From: </b>"Ali Nesin" <a href="mailto:anesin@nesinkoyleri.org" rel="nofollow noopener noreferrer nofollow noopener noreferrer nofollow noopener noreferrer 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 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 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 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 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 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 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 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:ii_19423d67e91531578ec3" alt=""></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_-726137518740113417m_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 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 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 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 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 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 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 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 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 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 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 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:ii_19423d67e91cb971f164" alt="image.png" style="width:277px;max-width:100%"><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:ii_19423d67e91cb971f165" alt="image.png" style="width:600px;max-width:100%"><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:ii_19423d67e91cb971f166" alt="image.png" style="width:760px;max-width:100%"><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 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_-726137518740113417m_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 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 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 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 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 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 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_-726137518740113417m_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 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 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 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 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 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_-726137518740113417m_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 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 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 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 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 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.
</blockquote></div></div></div></div></div></div></div></div></div></div></div></div></div></blockquote></div></div></div></div></div></div></div></blockquote></div></blockquote></div></div></blockquote></div></div></div></div></div></div></blockquote></div></div></blockquote></div></div></div></div></div></blockquote></div></div></div></blockquote></div></blockquote></div></div></div>