Georg Cantor nezm\u011bnil jen matematiku. Rozbil to. <\/p>\n
Tento n\u011bmeck\u00fd matematik narozen\u00fd v Petrohrad\u011b v roce 1845 se pod\u00edval na \u010d\u00edsla a vid\u011bl, co ostatn\u00edm uniklo. P\u0159ed n\u00edm bylo nekone\u010dno v\u00e1gn\u00ed pojem. Velk\u00e9 \u010d\u00edslo, kter\u00e9 trv\u00e1 v\u011b\u010dn\u011b. Ale Kantor v tom vid\u011bl m\u00edsto. Krajina s r\u016fzn\u00fdmi regiony, r\u016fzn\u00fdmi velikostmi a r\u016fzn\u00fdmi pravidly. <\/p>\n
Stal se zakladatelem teorie mno\u017ein<\/strong>, pova\u017eoval soustavy \u010d\u00edsel za integr\u00e1ln\u00ed objekty. Ned\u00edval se jen na jednotliv\u00e1 racion\u00e1ln\u00ed \u010d\u00edsla. Pod\u00edval se na celou skupinu. Na v\u0161echno spousta \u010d\u00edsel. Tento posun v perspektiv\u011b vedl k objevu, kter\u00fd dodnes plat\u00ed pro mnoho lid\u00ed. <\/p>\n Ne v\u0161echna nekone\u010dna jsou si rovna. <\/p>\n Cantor p\u0159edev\u0161\u00edm dok\u00e1zal, \u017ee n\u011bkter\u00e9 nekone\u010dn\u00e9 mno\u017einy lze spo\u010d\u00edtat. Vezm\u011bme racion\u00e1ln\u00ed \u010d\u00edsla. Toto jsou zlomky. Jak\u00e9koli \u010d\u00edslo, kter\u00e9 lze zapsat jako jedno cel\u00e9 \u010d\u00edslo d\u011blen\u00e9 druh\u00fdm. Zd\u00e1 se, \u017ee zlomk\u016f je mnohem v\u00edce ne\u017e p\u0159irozen\u00fdch \u010d\u00edsel (1, 2, 3…). <\/p>\n Cantor uk\u00e1zal osobn\u00ed korespondenci. Ka\u017ed\u00e9 racion\u00e1ln\u00ed \u010d\u00edslo p\u0159i\u0159adil k jedine\u010dn\u00e9mu p\u0159irozen\u00e9mu \u010d\u00edslu. Nic nez\u016fstane bez p\u00e1ru. Op\u011bt se nic nestalo. <\/p>\n Mno\u017eina racion\u00e1ln\u00edch \u010d\u00edsel je spo\u010detn\u00e1. <\/p>\n<\/blockquote>\n To znamenalo, \u017ee nekone\u010dno zlomk\u016f m\u011blo stejnou \u201evelikost\u201c jako nekone\u010dno cel\u00fdch \u010d\u00edsel. Matematici tomu \u0159\u00edkaj\u00ed spo\u010detn\u00e9 nekone\u010dno. D\u00e1 se to zvl\u00e1dnout. M\u016f\u017ee b\u00fdt uveden. D\u00e1 se o\u010d\u00edslovat. <\/p>\n Pak ale p\u0159i\u0161el po\u0159\u00e1dn\u00fd \u0161ok. <\/p>\n Cantor obr\u00e1til svou pozornost k iracion\u00e1ln\u00edm \u010d\u00edsl\u016fm. \u010c\u00edsla jako p\u00ed nebo druh\u00e1 odmocnina ze dvou. Tato desetinn\u00e1 m\u00edsta pokra\u010duj\u00ed nav\u017edy bez opakov\u00e1n\u00ed. Vypl\u0148uj\u00ed mezery mezi zlomky. Cantor dok\u00e1zal, \u017ee takov\u00e1 korespondence je zde nemo\u017en\u00e1. <\/p>\n Nem\u016f\u017eete je p\u0159i\u0159adit k p\u0159irozen\u00fdm \u010d\u00edsl\u016fm. Je jich prost\u011b moc. <\/p>\n Toto mno\u017estv\u00ed je nespo\u010detn\u00e9. Je v\u011bt\u0161\u00ed. Toto je v\u011bt\u0161\u00ed nekone\u010dno. <\/p>\n Tento objev vedl Cantora ke klasifikaci toho, co naz\u00fdval transfinitn\u00ed \u010d\u00edsla. To jsou stupn\u011b nekone\u010dna. <\/p>\n Pokud uva\u017eujete o nekone\u010dnu jako o v\u00fd\u0161ce, Cantor uk\u00e1zal, \u017ee to nen\u00ed jen jeden vysok\u00fd vrchol. Toto je poho\u0159\u00ed. N\u011bkter\u00e9 vrcholy jsou vy\u0161\u0161\u00ed ne\u017e jin\u00e9. Nekone\u010dno re\u00e1ln\u00fdch \u010d\u00edsel je vy\u0161\u0161\u00ed ne\u017e nekone\u010dno p\u0159irozen\u00fdch \u010d\u00edsel. <\/p>\n Nejen o tom h\u00e1dal. Pou\u017e\u00edval p\u0159\u00edsnou logiku. P\u0159\u00edmo porovn\u00e1val velikosti sad. Pokud m\u016f\u017eete beze zbytku porovnat ka\u017ed\u00fd prvek mno\u017einy A s prvkem mno\u017einy B, budou m\u00edt stejnou velikost. Pokud nem\u016f\u017eete, pak je jeden v\u011bt\u0161\u00ed ne\u017e druh\u00fd. <\/p>\n Proto je d\u016fle\u017eit\u00e9 pochopit Cantor\u016fv diagon\u00e1ln\u00ed argument<\/strong>. To je d\u016fkaz, \u017ee re\u00e1ln\u00e1 \u010d\u00edsla jsou nespo\u010d\u00edtateln\u00e1. Ukazuje konkr\u00e9tn\u00ed zp\u016fsob, jak naj\u00edt \u010d\u00edslo, kter\u00e9 nen\u00ed na \u017e\u00e1dn\u00e9m seznamu, kter\u00fd se pokou\u0161\u00edte vytvo\u0159it. <\/p>\n V\u011bt\u0161ina lid\u00ed na st\u0159edn\u00ed \u0161kole p\u0159estane o Cantorovi sly\u0161et. Nebo o tom nikdy nesly\u0161eli. U\u010d\u00ed se matematiku jako soubor statick\u00fdch pravidel. P\u0159id\u00e1n\u00ed. Od\u010d\u00edt\u00e1n\u00ed. N\u00e1soben\u00ed. Divize. <\/p>\n Cantor n\u00e1s u\u010d\u00ed, \u017ee matematika je dynamick\u00e1. Jde o vztahy mezi skupinami. A nejen o jednotliv\u00fdch \u010d\u00edslech. <\/p>\n Studiem z\u00e1klad\u016f teorie mno\u017ein<\/strong> se nau\u010d\u00edte myslet ve struktur\u00e1ch. Jak do sebe tyto \u010d\u00e1sti zapadaj\u00ed? Mohou se navz\u00e1jem mapovat? Co zbylo? <\/p>\n To nen\u00ed jen abstraktn\u00ed teorie. Informatika takto zpracov\u00e1v\u00e1 data. Takhle funguje logika. Takto ch\u00e1peme limity.<\/p>\n","protected":false},"excerpt":{"rendered":" Georg Cantor nezm\u011bnil jen matematiku. Rozbil to. Tento n\u011bmeck\u00fd matematik narozen\u00fd v Petrohrad\u011b v roce 1845 se pod\u00edval na \u010d\u00edsla a vid\u011bl, co ostatn\u00edm uniklo. P\u0159ed n\u00edm bylo nekone\u010dno v\u00e1gn\u00ed pojem. Velk\u00e9 \u010d\u00edslo, kter\u00e9 trv\u00e1 v\u011b\u010dn\u011b. Ale Kantor v tom vid\u011bl m\u00edsto. Krajina s r\u016fzn\u00fdmi regiony, r\u016fzn\u00fdmi velikostmi a r\u016fzn\u00fdmi pravidly. Stal se zakladatelem teorie […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":""},"categories":[50],"tags":[],"wpm_language_slugs":{"cs":"uzasna-matematika-nekonecnych-dimenzi-teorie-mnozin-georga-cantora","de":"die-uberraschende-mathematik-unendlicher-grosen-georg-cantors","en":"the-surprising-math-of-infinite-sizes-georg-cantors-set-theory","es":"la-sorprendente-matematica-de-los-tamanos-infinitos-explicacion-de","fr":"les-mathematiques-surprenantes-des-tailles-infinies-la-theorie-des","id":"matematika-mengejutkan-dengan-ukuran-tak-terbatas-penjelasan-teori","it":"la-sorprendente-matematica-delle-dimensioni-infinite-spiegazione-della","nl":"de-verrassende-wiskunde-van-oneindige-maten-de-verzamelingentheorie","pl":"niesamowita-matematyka-nieskonczonych-wymiarow-teoria-mnogosci","pt":"a-surpreendente-matematica-dos-tamanhos-infinitos-a-teoria-dos","ru-ru":"udivitelnaja-matematika-beskonechnyh-razmerov-teorija-mnozhestv-georga","uk-ua":"divovizhna-matematika-neskinchennih-rozmiriv-teorija-mnozhin-georga"},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/8041"}],"collection":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/comments?post=8041"}],"version-history":[{"count":0,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/8041\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media?parent=8041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/categories?post=8041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/tags?post=8041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Po\u010d\u00edt\u00e1n\u00ed nespo\u010ditateln\u00fdch<\/h2>\n
\n
Stupn\u011b nekone\u010dna<\/h2>\n
Pro\u010d je to d\u016fle\u017eit\u00e9 pro u\u010den\u00ed matematiky<\/h2>\n