{"id":3818,"date":"2023-02-05T12:33:39","date_gmt":"2023-02-05T09:33:39","guid":{"rendered":"https:\/\/blog.inekle.com\/?p=3818"},"modified":"2023-02-05T12:33:40","modified_gmt":"2023-02-05T09:33:40","slug":"hilbertin-sonsuz-odali-oteli","status":"publish","type":"post","link":"https:\/\/blog.inekle.com\/hilbertin-sonsuz-odali-oteli\/","title":{"rendered":"Hilbert&#8217;in Sonsuz Odal\u0131 Oteli"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u0130nsanlar\u0131 en \u00e7ok korkutan \u015fey nedir? \u00d6yle hemen tak diye cevap verilebilecek bir soru olmad\u0131\u011f\u0131n\u0131n fark\u0131nday\u0131m. Kimine g\u00f6re yaln\u0131zl\u0131k, kimine g\u00f6re mutsuzluk, kimine g\u00f6re ise paras\u0131zl\u0131k. Bu sayd\u0131klar\u0131m d\u00f6nen d\u00fcnyaya ayak uydurmaya \u00e7al\u0131\u015fan insan\u0131n, merkezine ald\u0131\u011f\u0131 baz\u0131 d\u00fc\u015f\u00fcnceleri. Bug\u00fcn burada d\u00f6nen d\u00fcnyay\u0131 bir kenara b\u0131rak\u0131p kendi d\u00fcnyas\u0131nda kendi sorular\u0131 ve merak\u0131yla, adeta k\u00fc\u00e7\u00fckken astronot olup uzaya \u00e7\u0131kmay\u0131 d\u00fc\u015f\u00fcnen bir \u00e7ocuk heyecan\u0131yla kendine bir otel kuran Hilberti ve onun sorular\u0131n\u0131 inceleyece\u011fiz. Sonsuza kadar sonsuzluk\u2026<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-6.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"365\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-6-1024x365.png\" alt=\"\" class=\"wp-image-3820\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-6-1024x365.png 1024w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-6-300x107.png 300w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-6-768x274.png 768w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-6.png 1200w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hilbert, merakl\u0131 bir insan olsa gerek, bundan y\u0131llar \u00f6nce bir otel h\u00e2yal etti, sonsuza kadar giden, sonsuz odas\u0131 olan bir otel. \u015e\u00f6yle ifade edebiliriz: Oda say\u0131s\u0131 1,2,3,4.. rakamlar\u0131yla ba\u015fl\u0131yor fakat herhangi bir yerde durmuyor, ne binlerde ne de milyonlarda.Evet b\u00f6yle bir \u015feyin olmas\u0131 teorik olarak m\u00fcmk\u00fcn de\u011fil, bunu o da biliyor. Hatta d\u00fc\u015f\u00fcnd\u00fck\u00e7e ve o oteli hayal ettik\u00e7e i\u015fler karmakar\u0131\u015f\u0131kla\u015f\u0131yor.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-8.png\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"444\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-8.png\" alt=\"\" class=\"wp-image-3822\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-8.png 800w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-8-300x167.png 300w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-8-768x426.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Bu Hilbert denilen adam ne kadar \u015fansl\u0131 ki sonsuz odas\u0131 olan sonsuzluk oteli, daha ilk g\u00fcnlerden tam doluyor (Her oda bir ki\u015filiktir.). Sonsuz odal\u0131, sonsuz m\u00fc\u015fterili bir otel\u2026 Her \u015fey yolunda giderken bu otele bir m\u00fc\u015fteri daha geliyor. Resepsiyon g\u00f6revlisi tam m\u00fc\u015fteriyi geri \u00e7evirecek ki akl\u0131na muazzam bir fikir geliyor.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-9.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-9-1024x576.png\" alt=\"\" class=\"wp-image-3823\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-9-1024x576.png 1024w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-9-300x169.png 300w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-9-768x432.png 768w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-9.png 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0130lk olarak sonsuz odas\u0131 olan bir otelde \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131 hat\u0131rl\u0131yor, daha sonra 1. odadaki m\u00fc\u015fteriyi 2. odaya, 2. odadaki m\u00fc\u015fteriyi 3. odaya, 3. odadaki m\u00fc\u015fteriyi 4. odaya, bu \u015fekilde devam ederek, yeni gelen m\u00fc\u015fteriyi 1.odaya yerle\u015ftiriyor. Tam sorunu \u00e7\u00f6zd\u00fcm derken ne g\u00f6rs\u00fcn, sonsuz m\u00fc\u015fterisi olan bir otob\u00fcs otele do\u011fru gelmekte.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-10.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-10.png\" alt=\"\" class=\"wp-image-3824\" width=\"835\" height=\"469\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-10.png 648w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-10-300x169.png 300w\" sizes=\"auto, (max-width: 835px) 100vw, 835px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Biraz d\u00fc\u015f\u00fcnd\u00fckten sonra, gelen m\u00fc\u015fterileri de oteline almay\u0131 ba\u015far\u0131yor. Resepsiyon g\u00f6revlisi, 1. odadaki m\u00fc\u015fteriyi 2. odaya, 2. odadaki m\u00fc\u015fteriyi 4. odaya, 3. odadaki m\u00fc\u015fteriyi 6. odaya, yani oteldeki m\u00fc\u015fterileri oda numaras\u0131 tek say\u0131 olanlara yerle\u015ftiriyor. Di\u011fer gelen sonsuz m\u00fc\u015fterileri de 1. m\u00fc\u015fteriyi 1.odaya, 2. m\u00fc\u015fteriyi 3. odaya, 3. m\u00fc\u015fteriyi 5. odaya, bu \u015fekilde devam ederek m\u00fc\u015fterileri odalara yerle\u015ftiriyor. Buradaki matematiksel d\u00fc\u015f\u00fcncesi tek say\u0131lar\u0131n ve \u00e7ift say\u0131lar\u0131n sonsuza kadar gitti\u011fini bilmesinden geliyor. Ayr\u0131ca hem tek hem \u00e7ift olan bir say\u0131 olmamas\u0131 da olas\u0131 bir ayn\u0131 odaya farkl\u0131 farkl\u0131 m\u00fc\u015fteriler yerle\u015ftirmesi durumunu engelliyor. Ger\u00e7ekten matematik bilen bir resepsiyon g\u00f6revlisi olmas\u0131, hem otelin hem de kendisinin sonsuz miktarda para kazanmas\u0131na olanak sa\u011fl\u0131yor.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-11.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-11.png\" alt=\"\" class=\"wp-image-3825\" width=\"838\" height=\"471\" srcset=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-11.png 500w, https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-11-300x169.png 300w\" sizes=\"auto, (max-width: 838px) 100vw, 838px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Daha ileri bir a\u015fama olan sonsuz otob\u00fcste sonsuz m\u00fc\u015fteri gelmesi durumunu bir sonraki yaz\u0131da inceleyece\u011fiz. Resepsiyon g\u00f6revlisi siz olsayd\u0131n\u0131z bu otele sonsuz say\u0131da otob\u00fcste gelen sonsuz m\u00fc\u015fterileri nas\u0131l yerle\u015ftirirdiniz?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bol \u015fans\u2026 \ud83d\ude42<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Emre Kahraman<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-12.png\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/blog.inekle.com\/wp-content\/uploads\/2023\/02\/image-12.png\" alt=\"\" class=\"wp-image-3826\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">05.02.2023<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130nsanlar\u0131 en \u00e7ok korkutan \u015fey nedir? \u00d6yle hemen tak diye cevap verilebilecek bir soru olmad\u0131\u011f\u0131n\u0131n fark\u0131nday\u0131m. Kimine g\u00f6re yaln\u0131zl\u0131k, kimine g\u00f6re mutsuzluk,\u2026<\/p>\n","protected":false},"author":1,"featured_media":3819,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[380,50,7,1113,102,88],"tags":[708,702,22,1950,641,711,163,42,154,1747,686,70,151,685],"class_list":["post-3818","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ogrenciler-soruyor","category-online-egitim","category-sinavlar","category-sks","category-vay-canina","category-veliler-icin","tag-ayt","tag-blog","tag-canli-ders","tag-hilbertin-sonsuz-odali-oteli","tag-inekle","tag-lgs","tag-lys-tavsiyeleri","tag-matematik","tag-online-ozel-ders","tag-teorisi","tag-tyt","tag-universite-tercih","tag-universiteliden-ozel-ders","tag-yks"],"_links":{"self":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/posts\/3818","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/comments?post=3818"}],"version-history":[{"count":0,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/posts\/3818\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/media\/3819"}],"wp:attachment":[{"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/media?parent=3818"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/categories?post=3818"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.inekle.com\/wp-json\/wp\/v2\/tags?post=3818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}