Bir k\u00fcmedeki eleman say\u0131s\u0131yla do\u011fal say\u0131lar aras\u0131nda birebir e\u015fleme kurulabilme durumu. 19. y\u00fczy\u0131l\u0131n sonlar\u0131na kadar matematikte farkl\u0131 b\u00fcy\u00fckl\u00fcklerde sonsuzlar\u0131n olabilece\u011finden \u015f\u00fcphelenilmiyordu. Ancak Alman matematik\u00e7i Georg Cantor’un reel say\u0131lar\u0131n say\u0131lamayaca\u011f\u0131n\u0131 ispatlamas\u0131n\u0131n ard\u0131ndan matematikte farkl\u0131 b\u00fcy\u00fckl\u00fcklerde sonsuzluklar\u0131n var oldu\u011fu anla\u015f\u0131ld\u0131. Peki iki sonsuz say\u0131y\u0131 kar\u015f\u0131la\u015ft\u0131rmaktan anla\u015f\u0131lan nedir? Diyelim ki elimizde A ve B isimli iki sonsuz k\u00fcme var ve bunlar\u0131n eleman say\u0131lar\u0131na s\u0131ras\u0131yla a ve b diyelim. E\u011fer A k\u00fcmesinden B k\u00fcmesine birebir bir fonksiyon tan\u0131mlanabiliyorsa bu durumda denir. Bu tan\u0131m Se\u00e7im Aksiyomu’nun varsay\u0131ld\u0131\u011f\u0131 durumlarda bize sonsuz b\u00fcy\u00fckl\u00fckler aras\u0131nda bir do\u011frusal s\u0131ralama verir, yani k\u0131saca b\u00fct\u00fcn sonsuzluklar birbiriyle kar\u015f\u0131la\u015ft\u0131r\u0131labilirdir. \u0130\u015fte bu durumda, say\u0131labilirlik en k\u00fc\u00e7\u00fck sonsuz b\u00fcy\u00fckl\u00fc\u011f\u00fc ifade eder, ancak baz\u0131 yazarlar say\u0131labilirli\u011fi ayn\u0131 zamanda “ya sonlu ya da say\u0131labilir sonsuz olma” durumu i\u00e7in de kullan\u0131rlar. S\u00fcreklilik Hipotezi ise do\u011fal say\u0131lar\u0131n k\u00fcmesinin b\u00fcy\u00fckl\u00fc\u011f\u00fc ile reel say\u0131lar\u0131n k\u00fcmesinin b\u00fcy\u00fckl\u00fc\u011f\u00fc aras\u0131nda ba\u015fka b\u00fcy\u00fckl\u00fck olmad\u0131\u011f\u0131n\u0131 ifade eden aksiyomdur.
\n Say\u0131labilir k\u00fcmelere \u00f6rnekler:
\nDo\u011fal say\u0131lar
\nTam say\u0131lar
\nOranl\u0131 say\u0131lar
\nAsal say\u0131lar
\nSay\u0131lamaz k\u00fcmelere \u00f6rnekler:
\nGer\u00e7el say\u0131lar
\nKarma\u015f\u0131k say\u0131lar
\nCantor’un k\u00fcmesi
\nDo\u011fal say\u0131lar\u0131n alt k\u00fcmelerinin k\u00fcmesi<\/p>\n","protected":false},"excerpt":{"rendered":"
Bir k\u00fcmedeki eleman say\u0131s\u0131yla do\u011fal say\u0131lar aras\u0131nda birebir e\u015fleme kurulabilme durumu. 19. y\u00fczy\u0131l\u0131n sonlar\u0131na kadar matematikte farkl\u0131 b\u00fcy\u00fckl\u00fcklerde sonsuzlar\u0131n olabilece\u011finden \u015f\u00fcphelenilmiyordu. Ancak Alman matematik\u00e7i Georg Cantor’un reel say\u0131lar\u0131n say\u0131lamayaca\u011f\u0131n\u0131 ispatlamas\u0131n\u0131n ard\u0131ndan matematikte farkl\u0131 b\u00fcy\u00fckl\u00fcklerde sonsuzluklar\u0131n var oldu\u011fu anla\u015f\u0131ld\u0131. Peki iki sonsuz say\u0131y\u0131 kar\u015f\u0131la\u015ft\u0131rmaktan anla\u015f\u0131lan nedir? Diyelim ki elimizde A ve B isimli iki sonsuz k\u00fcme …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7208,7385,7469,7391,7468,2782,7467,7426],"class_list":["post-3222","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-asal-sayilar","tag-dogal-sayilar","tag-gercel-sayilar","tag-karmasik-sayilar","tag-oranli-sayilar","tag-reel-sayilar","tag-sayilabilirlik","tag-tam-sayilar"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3222","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3222"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3222\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}