{"id":346,"date":"2018-11-22T16:52:09","date_gmt":"2018-11-22T15:52:09","guid":{"rendered":"https:\/\/nadvakroky.sk\/?p=346"},"modified":"2018-11-22T16:52:09","modified_gmt":"2018-11-22T15:52:09","slug":"hilbertov-paradox-nekonecneho-hotela","status":"publish","type":"post","link":"https:\/\/wp1.science.upjs.sk\/nadvakrorky\/2018\/11\/22\/hilbertov-paradox-nekonecneho-hotela\/","title":{"rendered":"Hilbertov paradox nekone\u010dn\u00e9ho hotela"},"content":{"rendered":"<p><span style=\"font-weight: 400\">Ak by mal hotel kone\u010dn\u00fd po\u010det izieb, zrejme by sme nov\u00e9ho hos\u0165a nevedeli prija\u0165. Izieb je v\u0161ak nekone\u010dno, a preto jednoducho po\u017eiadame ka\u017ed\u00e9ho hos\u0165a, aby sa pres\u0165ahoval o izbu \u010falej. Hos\u0165 z prvej izby sa pres\u0165ahuje do druhej, hos\u0165 z druhej izby do tretej a tak \u010falej. Pre nov\u00e9ho hos\u0165a sa tak uvo\u013en\u00ed prv\u00e1 izba.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Podobn\u00fdm sp\u00f4sobom vieme ubytova\u0165 ak\u00fdko\u013evek kone\u010dn\u00fd po\u010det nov\u00fdch hos\u0165ov. <strong>Ako v\u0161ak postupova\u0165 v pr\u00edpade, \u017ee do hotela pr\u00edde nekone\u010dne ve\u013ea nov\u00fdch host\u00ed? <\/strong><\/span><\/p>\n<p><span style=\"font-weight: 400\">Uk\u00e1\u017eme si najjednoduch\u0161\u00ed sp\u00f4sob: hos\u0165a z izby \u010d. 1 po\u0161leme do izby \u010d. 2, hos\u0165a z izby \u010d. 2 do izby \u010d. 4, hos\u0165a z n-tej izby do 2n-tej:<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-weight: 400\">1 \u2192 2<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-weight: 400\">2 \u2192 4<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-weight: 400\">3 \u2192 6<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-weight: 400\">4 \u2192 8<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-weight: 400\">\u2026<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-weight: 400\">n \u2192 2n<\/span><\/p>\n<p><span style=\"font-weight: 400\"><strong>Takto sa n\u00e1m uvo\u013en\u00ed nekone\u010dne ve\u013ea izieb.<\/strong> <\/span><\/p>\n<p><span style=\"font-weight: 400\">Kde sa skr\u00fdva paradox? Aj ke\u010f n\u00e1m intu\u00edcia vrav\u00ed, \u017ee prirodzen\u00fdch \u010d\u00edsel je dvakr\u00e1t viac ne\u017e p\u00e1rnych prirodzen\u00fdch \u010d\u00edsel, nie je to pravda. <strong>P\u00e1rnych \u010d\u00edsel nie je menej ako prirodzen\u00fdch: \u201epo\u010det\u201c oboch ozna\u010dujeme ako spo\u010d\u00edtate\u013en\u00e9 nekone\u010dno.<\/strong><\/span><\/p>\n<p>Pr\u00edspevok pripravila b\u00fdval\u00e1 \u0161tudentka UPJ\u0160 &#8211; <strong>Mgr. Lucia Keke\u0148\u00e1kov\u00e1<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ak by mal hotel kone\u010dn\u00fd po\u010det izieb, zrejme by sme nov\u00e9ho hos\u0165a nevedeli prija\u0165. Izieb je v\u0161ak nekone\u010dno, a preto jednoducho po\u017eiadame ka\u017ed\u00e9ho hos\u0165a, aby sa pres\u0165ahoval o izbu \u010falej. Hos\u0165 z prvej izby sa pres\u0165ahuje do druhej, hos\u0165 z druhej izby do tretej a tak \u010falej. Pre nov\u00e9ho hos\u0165a sa tak uvo\u013en\u00ed prv\u00e1 izba. [&hellip;]<\/p>\n","protected":false},"author":93,"featured_media":347,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[14],"tags":[],"class_list":["post-346","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Hilbertov paradox nekone\u010dn\u00e9ho hotela - Nadvakroky.sk<\/title>\n<meta name=\"description\" content=\"Paradoxy te\u00f3rie mno\u017e\u00edn. 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