@prefix dbo: .
@prefix dbr: .
dbr:Reductionism dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Hyperreal_number dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Space-filling_curve dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:David_Hilbert dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Paul_Mahlo dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Foundations_of_mathematics dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Transfinite_number dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Constructible_universe dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Second-order_logic dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Cardinal_number dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Paul_Cohen dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
@prefix dbp: .
dbr:Paul_Cohen dbp:knownFor dbr:Continuum_hypothesis ;
dbo:knownFor dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Infinitary_logic dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:List_of_mathematical_logic_topics dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:List_of_set_theory_topics dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Inaccessible_cardinal dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Vaught_conjecture dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Fallibilism dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbr:Dana_Scott dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Leon_Henkin dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:International_Congress_of_Mathematicians dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Uncountable_set dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Adolf_Lindenbaum dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Generic_filter dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Regular_cardinal dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
@prefix foaf: .
@prefix wikipedia-en: .
wikipedia-en:Continuum_hypothesis foaf:primaryTopic dbr:Continuum_hypothesis .
dbr:Logic dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Box_topology dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Outline_of_logic dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Truth dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:List_of_important_publications_in_mathematics dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Equiconsistency dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Spectrum_of_a_theory dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Universally_Baire_set dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Infinity dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:History_of_mathematics dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Number dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Real_number dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Cardinality dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Set_theory dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Axiom dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Whitehead_problem dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Saharon_Shelah dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Certainty dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:History_of_logic dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Conjecture dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbr:Set_theory_of_the_real_line dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbr:Cofinality dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbr:Parovicenko_space dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Set-theoretic_topology dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Ignoramus_et_ignorabimus dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Jewish_culture dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Large_numbers dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbr:Condensation_lemma dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Continuum dbo:wikiPageWikiLink dbr:Continuum_hypothesis ;
dbo:wikiPageDisambiguates dbr:Continuum_hypothesis .
dbr:Transcendence_degree dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Real_closed_field dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Mathematical_logic dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Model_theory dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Axiom_of_choice dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Timeline_of_Polish_science_and_technology dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:List_of_forcing_notions dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Beth_number dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Ontological_maximalism dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Gimel_function dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Continuum_function dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbr:Dialetheism dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Franciscus_Patricius dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Clubsuit dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Generalized_Continuum_Hypothesis dbo:wikiPageWikiLink dbr:Continuum_hypothesis ;
dbo:wikiPageRedirects dbr:Continuum_hypothesis .
dbr:Cardinality_of_the_continuum dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Conservative_extension dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:History_of_topos_theory dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
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dbr:List_of_axioms dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Opaque_set dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Ramified_forcing dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Generalised_continuum_hypothesis dbo:wikiPageWikiLink dbr:Continuum_hypothesis ;
dbo:wikiPageRedirects dbr:Continuum_hypothesis .
dbr:Cardinal_and_Ordinal_Numbers dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis ;
dbo:knownFor dbr:Continuum_hypothesis .
dbr:Antiphilosophy dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:List_of_continuity-related_mathematical_topics dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Ernst_Zermelo dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Perfect_set_property dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:List_of_statements_independent_of_ZFC dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Axiom_of_constructibility dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Generalized_continuum_hypothesis dbo:wikiPageWikiLink dbr:Continuum_hypothesis ;
dbo:wikiPageRedirects dbr:Continuum_hypothesis .
dbr:Philosophy_of_mathematics dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Fields_Medal dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Alain_Badiou dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Undecidable_problem dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:Strong_measure_zero_set dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbo:wikiPageWikiLink dbr:Continuum_hypothesis .
dbr:CH dbo:wikiPageWikiLink dbr:Continuum_hypothesis ;
dbo:wikiPageDisambiguates dbr:Continuum_hypothesis .
@prefix rdf: .
@prefix yago: .
dbr:Continuum_hypothesis rdf:type yago:Idea105833840 ,
yago:Content105809192 ,
yago:Problem114410605 ,
yago:DefiniteQuantity113576101 ,
yago:Concept105835747 ,
yago:Number113582013 ,
yago:Proposal107162194 ,
yago:Hypothesis107162545 ,
yago:Message106598915 ,
yago:Cognition100023271 ,
yago:Abstraction100002137 .
@prefix owl: .
dbr:Continuum_hypothesis rdf:type owl:Thing ,
yago:PsychologicalFeature100023100 ,
yago:WikicatCardinalNumbers ,
yago:WikicatHypotheses ,
yago:WikicatBasicConceptsInInfiniteSetTheory ,
yago:CardinalNumber113597585 ,
yago:Saying107151380 ,
yago:WikicatAxiomsOfSetTheory ,
yago:Communication100033020 ,
yago:AuditoryCommunication107109019 ,
dbo:Book ,
yago:Maxim107152948 ,
yago:Difficulty114408086 ,
yago:Measure100033615 ,
yago:Condition113920835 ,
,
yago:Attribute100024264 ,
yago:State100024720 ,
yago:Speech107109196 .
@prefix rdfs: .
dbr:Continuum_hypothesis rdfs:label "Ipotesi del continuo"@it ,
"Continuum hypothesis"@en ,
"\u041A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0438\u043F\u043E\u0442\u0435\u0437\u0430"@ru ,
"Kontinuumhypotesen"@sv ,
"Kontinua\u0135a hipotezo"@eo ,
"\u8FDE\u7EED\u7EDF\u5047\u8BBE"@zh ,
"Hipotesis kontinum"@in ,
"Hypoth\u00E8se du continu"@fr ,
"Hip\u00F2tesi del continu"@ca ,
"Hypot\u00E9za kontinua"@cs ,
"Kontinuumshypothese"@de ,
"Continu\u00FCmhypothese"@nl ,
"Hipoteza continuum"@pl ,
"\uC5F0\uC18D\uCCB4 \uAC00\uC124"@ko ,
"\u9023\u7D9A\u4F53\u4EEE\u8AAC"@ja ,
"\u041A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430"@uk ,
"\u0641\u0631\u0636\u064A\u0629 \u0627\u0644\u0627\u0633\u062A\u0645\u0631\u0627\u0631\u064A\u0629"@ar ,
"Hip\u00F3tese do continuum"@pt ,
"\u03A5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03B5\u03C7\u03BF\u03CD\u03C2"@el ,
"Hip\u00F3tesis del continuo"@es ;
rdfs:comment "\u9023\u7E8C\u7D71\u5047\u8A2D\uFF08\u82F1\u8A9E\uFF1AContinuum hypothesis\uFF0C\u7C21\u7A31CH\uFF09\u662F\u6570\u5B66\u4E2D\u4E00\u500B\u731C\u60F3\uFF0C\u4E5F\u662F\u5E0C\u5C14\u4F2F\u7279\u768423\u4E2A\u95EE\u9898\u7684\u7B2C\u4E00\u984C\uFF0C\u7531\u5EB7\u6258\u5C14\u63D0\u51FA\uFF0C\u95DC\u65BC\u7121\u7AAE\u96C6\u7684\u53EF\u80FD\u5927\u5C0F\u3002\u5176\u70BA\uFF1A \u4E0D\u5B58\u5728\u4E00\u500B\u57FA\u6570\u7D55\u5C0D\u5927\u4E8E\u53EF\u6578\u96C6\u800C\u7D55\u5C0D\u5C0F\u4E8E\u5B9E\u6570\u96C6\u7684\u96C6\u5408\u3002 \u5EB7\u6258\u723E\u5F15\u5165\u4E86\u57FA\u6578\u7684\u6982\u5FF5\u4EE5\u6BD4\u8F03\u7121\u7AAE\u96C6\u9593\u7684\u5927\u5C0F\uFF0C\u4E5F\u8B49\u660E\u4E86\u6574\u6578\u96C6\u7684\u57FA\u6578\u7D55\u5C0D\u5C0F\u65BC\u5BE6\u96C6\u7684\u57FA\u6578\u3002\u5EB7\u6258\u723E\u4E5F\u5C31\u7D66\u51FA\u4E86\u9023\u7E8C\u7D71\u5047\u8A2D\uFF0C\u5C31\u662F\u8BF4\uFF0C\u5728\u65E0\u9650\u96C6\u4E2D\uFF0C\u6BD4\u81EA\u7136\u6570\u96C6\u57FA\u6570\u5927\u7684\u96C6\u5408\u4E2D\uFF0C\u57FA\u6570\u6700\u5C0F\u7684\u96C6\u5408\u662F\u5B9E\u6570\u96C6\u3002\u800C\u9023\u7E8C\u7D71\u5C31\u662F\u5BE6\u6578\u96C6\u7684\u4E00\u500B\u820A\u7A31\u3002 \u66F4\u52A0\u5F62\u5F0F\u5730\u8BF4\uFF0C\u81EA\u7136\u6570\u96C6\u7684\u57FA\u6570\u4E3A\uFF08\u8B80\u4F5C\u300C\u963F\u5217\u592B\u96F6\u300D\uFF09\u3002\u800C\u8FDE\u7EED\u7EDF\u5047\u8BBE\u7684\u89C2\u70B9\u8BA4\u4E3A\u5B9E\u6570\u96C6\u7684\u57FA\u6570\u4E3A\uFF08\u8B80\u4F5C\u300C\u963F\u5217\u592B\u58F9\u300D\uFF09\u3002\u4E8E\u662F\uFF0C\u5EB7\u6258\u5C14\u5B9A\u4E49\u4E86\u7EDD\u5BF9\u65E0\u9650\u3002 \u7B49\u50F9\u5730\uFF0C\u6574\u6578\u96C6\u7684\u57FA\u6570\u662F\u800C\u5BE6\u6578\u7684\u57FA\u6570\u662F\uFF0C\u9023\u7E8C\u7D71\u5047\u8A2D\u6307\u51FA\u4E0D\u5B58\u5728\u4E00\u500B\u96C6\u5408\u4F7F\u5F97 \u5047\u8A2D\u9078\u64C7\u516C\u7406\u662F\u5C0D\u7684\uFF0C\u90A3\u5C31\u6703\u6709\u4E00\u500B\u6700\u5C0F\u7684\u57FA\u6578\u5927\u65BC\uFF0C\u800C\u9023\u7E8C\u7D71\u5047\u8A2D\u4E5F\u5C31\u7B49\u50F9\u65BC\u4EE5\u4E0B\u7684\u7B49\u5F0F\uFF1A \u9023\u7E8C\u7D71\u5047\u8A2D\u6709\u500B\u66F4\u5EE3\u7FA9\u7684\u5F62\u5F0F\uFF0C\u53EB\u4F5C\u5EE3\u7FA9\u9023\u7E8C\u7D71\u5047\u8A2D\uFF08GCH\uFF09\uFF0C\u5176\u547D\u984C\u70BA\uFF1A \u5BF9\u4E8E\u6240\u6709\u7684\u5E8F\u6570, \u5EAB\u723E\u7279\u00B7\u54E5\u5FB7\u5C14\u57281940\u5E74\u7528\u5185\u6A21\u578B\u6CD5\u8BC1\u660E\u4E86\u8FDE\u7EED\u7EDF\u5047\u8BBE\u4E0EZFC\u7684\u76F8\u5BF9\u534F\u8C03\u6027\uFF08\u7121\u6CD5\u4EE5ZFC\u8B49\u660E\u70BA\u8AA4\uFF09\uFF0C\u4FDD\u7F85\u00B7\u67EF\u6069\u57281963\u5E74\u7528\u529B\u8FEB\u6CD5\u8BC1\u660E\u4E86\u8FDE\u7EED\u7EDF\u5047\u8BBE\u4E0D\u80FD\u7531ZFC\u63A8\u5BFC\u3002\u4E5F\u5C31\u662F\u8BF4\u8FDE\u7EED\u7EDF\u5047\u8BBE\u65BCZFC\u3002"@zh ,
"Hipoteza continuum (CH, ang. continuum hypothesis) \u2013 hipoteza teorii mnogo\u015Bci dotycz\u0105ca mocy zbior\u00F3w liczb naturalnych i liczb rzeczywistych. M\u00F3wi ona, \u017Ce pomi\u0119dzy nimi nie ma \u017Cadnej wielko\u015Bci po\u015Bredniej; innymi s\u0142owy \u2013 continuum to najmniejsza liczba nieprzeliczalna, co formu\u0142uje si\u0119 r\u00F3wnaniem: . Hipotez\u0119 t\u0119 sformu\u0142owa\u0142 w XIX wieku Georg Cantor; znalaz\u0142a si\u0119 ona w\u015Br\u00F3d problem\u00F3w Hilberta, jako pierwsza na li\u015Bcie. W XX wieku udowodniono, \u017Ce problem ten jest nierozstrzygalny dla standardowej teorii mnogo\u015Bci, tj. niezale\u017Cny od aksjomat\u00F3w Zermela-Fraenkla."@pl ,
"\u0641\u0631\u0636\u064A\u0629 \u0627\u0644\u0627\u062A\u0635\u0627\u0644\u064A\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: continuum hypothesis)\u200F \u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0648\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u062D\u062F\u0633\u064A\u0629 \u0627\u0644\u0627\u062A\u0635\u0627\u0644\u064A\u0629 \u0648\u062A\u062E\u062A\u0635\u0631 CH\u060C \u0647\u064A \u062A\u0635\u0648\u0631 \u0648\u0636\u0639\u0647 \u0627\u0644\u0631\u064A\u0627\u0636\u064A \u062C\u0648\u0631\u062C \u0643\u0627\u0646\u062A\u0648\u0631 \u0639\u0627\u0645 1878\u0639\u0646 \u0627\u0644\u0623\u062D\u062C\u0627\u0645 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0644\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064A\u0629. \u0648\u062A\u0646\u0635 \u0639\u0644\u0649: (\u0644\u0627 \u064A\u0648\u062C\u062F \u0645\u062C\u0645\u0648\u0639\u0629 \u0639\u062F\u062F \u0639\u0646\u0627\u0635\u0631\u0647\u0627 \u0627\u0644\u0623\u0635\u0644\u064A\u0629 \u0645\u062D\u062F\u062F\u0629 \u0628\u0634\u0643\u0644 \u0635\u0627\u0631\u0645 \u0628\u064A\u0646 \u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u0635\u062D\u064A\u062D\u0629 \u0648\u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u062D\u0642\u064A\u0642\u064A\u0629). \u0625\u0646 \u062D\u062F\u0633\u064A\u0629 \u0627\u0644\u0627\u062A\u0635\u0627\u0644\u064A\u0629 \u0644\u0643\u0627\u0646\u062A\u0648\u0631 \u0647\u064A \u0628\u0628\u0633\u0627\u0637\u0629 \u0627\u0644\u062A\u0633\u0627\u0624\u0644: \u0643\u0645 \u0639\u062F\u062F \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u0645\u0648\u062C\u0648\u062F\u0629 \u0639\u0644\u0649 \u062E\u0637 \u0645\u0633\u062A\u0642\u064A\u0645 \u0641\u064A \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0625\u0642\u0644\u064A\u062F\u064A\u061F \u0623\u0648 \u0628\u0635\u064A\u063A\u0629 \u0623\u062E\u0631\u0649: \u0643\u0645 \u0639\u062F\u062F \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u0645\u062E\u062A\u0644\u0641\u0629 \u0627\u0644\u0645\u0648\u062C\u0648\u062F\u0629 \u0644\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u0635\u062D\u064A\u062D\u0629\u061F \u0641\u0647\u064A \u062A\u0633\u0627\u0624\u0644 \u0639\u0646 \u0645\u0642\u062F\u0627\u0631 \u0623\u0648 \u062D\u062C\u0645 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064A\u0629."@ar ,
"\u9023\u7D9A\u4F53\u4EEE\u8AAC\uFF08\u308C\u3093\u305E\u304F\u305F\u3044\u304B\u305B\u3064\u3001Continuum hypothesis, CH\uFF09\u3068\u306F\u3001\u53EF\u7B97\u6FC3\u5EA6\u3068\u9023\u7D9A\u4F53\u6FC3\u5EA6\u306E\u9593\u306B\u306F\u4ED6\u306E\u6FC3\u5EA6\u304C\u5B58\u5728\u3057\u306A\u3044\u3068\u3059\u308B\u4EEE\u8AAC\u300219\u4E16\u7D00\u306B\u30B2\u30AA\u30EB\u30AF\u30FB\u30AB\u30F3\u30C8\u30FC\u30EB\u306B\u3088\u3063\u3066\u63D0\u5531\u3055\u308C\u305F\u3002\u73FE\u5728\u306E\u6570\u5B66\u3067\u7528\u3044\u3089\u308C\u308B\u6A19\u6E96\u7684\u306A\u67A0\u7D44\u307F\u306E\u3082\u3068\u3067\u306F\u300C\u9023\u7D9A\u4F53\u4EEE\u8AAC\u306F\u8A3C\u660E\u3082\u53CD\u8A3C\u3082\u3067\u304D\u306A\u3044\u547D\u984C\u3067\u3042\u308B\u300D\u3068\u3044\u3046\u3053\u3068\u304C\u660E\u78BA\u306B\u8A3C\u660E\u3055\u308C\u3066\u3044\u308B\u3002"@ja ,
"In de verzamelingenleer, een deelgebied van de wiskunde, is de continu\u00FCmhypothese een door Georg Cantor in 1877 geponeerde hypothese over de mogelijke kardinaliteiten van oneindige verzamelingen. De hypothese luidt dat: Er bestaat geen verzameling, waarvan de kardinaliteit tussen de kardinaliteit van de gehele getallen en de kardinaliteit van de re\u00EBle getallen ligt."@nl ,
"En teor\u00EDa de conjuntos, la hip\u00F3tesis del continuo (tambi\u00E9n conocida como primer problema de Hilbert) es un enunciado relativo a la cardinalidad del conjunto de los n\u00FAmeros reales, formulado como una hip\u00F3tesis por Georg Cantor en 1878. Su enunciado afirma que no existen conjuntos infinitos cuyo tama\u00F1o est\u00E9 estrictamente comprendido entre el del conjunto de los n\u00FAmeros naturales y el del conjunto de los reales. El nombre continuo hace referencia al conjunto de los reales."@es ,
"En teoria de conjunts, la hip\u00F2tesi del continu (abreviada HC) \u00E9s una hip\u00F2tesi, proposada per Georg Cantor, sobre la cardinalitat del conjunt dels nombres reals (denominat continu per la recta real). Cantor introdu\u00ED el concepte de nombre cardinal per comparar la mida de conjunts infinits, demostrant el 1874 que el cardinal del conjunt dels enters \u00E9s estrictament inferior al dels nombres reals. El seg\u00FCent a preguntar-se \u00E9s si existeixen conjunts tals que la seva cardinalitat estigui estrictament inclosa entre els dos conjunts. La hip\u00F2tesi del continu diu: on |A| indica el cardinal d'A."@ca ,
"En th\u00E9orie des ensembles, l'hypoth\u00E8se du continu (HC), due \u00E0 Georg Cantor, affirme qu'il n'existe aucun ensemble dont le cardinal est strictement compris entre le cardinal de l'ensemble des entiers naturels et celui de l'ensemble des nombres r\u00E9els. En d'autres termes : tout ensemble strictement plus grand, au sens de la cardinalit\u00E9, que l'ensemble des entiers naturels doit contenir une \u00AB copie \u00BB de l'ensemble des nombres r\u00E9els."@fr ,
"En matematiko, la kontinua\u0135a hipotezo (iam mallonge CH) estas hipotezo pri la eblaj ampleksoj de malfiniaj aroj. \u011Ci asertas ke ne ekzistas aro kies kardinalo estas severe inter kardinalo de aro de entjeroj kaj kardinalo de aro de reelaj nombroj. La hipetezo estas de Georg Cantor de 1877. Kontrolado de vereco a\u016D malvereco de la kontinua\u0135a hipotezo estas la unua el la 23 prezentitaj en 1900. Laboroj de Kurt G\u00F6del en 1940 kaj en 1963 montris ke la hipotezo povas esti nek pruvita nek malpruvita uzante la aksiomojn de , la norma fundamento de moderna matematiko, se la aroteorio estas konsekvenca."@eo ,
"Hypot\u00E9za kontinua (ozna\u010Dovan\u00E1 n\u011Bkdy jako CH (z anglick\u00E9ho Continuum Hypothesis)) je matematick\u00E9 tvrzen\u00ED formulovan\u00E9 poprv\u00E9 Georgem Cantorem v roce 1882. Toto tvrzen\u00ED se t\u00FDk\u00E1 ot\u00E1zky, zda existuje n\u011Bjak\u00E1 mno\u017Eina, jej\u00ED\u017E mohutnost je ost\u0159e mezi mohutnost\u00ED mno\u017Einy p\u0159irozen\u00FDch \u010D\u00EDsel a mohutnost\u00ED mno\u017Einy \u010D\u00EDsel re\u00E1ln\u00FDch (neboli kontinua), a odpov\u00EDd\u00E1 na ni z\u00E1porn\u011B."@cs ,
"\u03A3\u03C4\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC, \u03B7 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03B5\u03C7\u03BF\u03CD\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B1 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7 \u03C3\u03C7\u03B5\u03C4\u03B9\u03BA\u03AC \u03BC\u03B5 \u03C4\u03B1 \u03C0\u03B9\u03B8\u03B1\u03BD\u03AC \u03BC\u03B5\u03B3\u03AD\u03B8\u03B7 \u03C4\u03C9\u03BD \u03B1\u03C0\u03B5\u03AF\u03C1\u03C9\u03BD \u03C3\u03CD\u03BD\u03BF\u03BB\u03C9\u03BD. \u0395\u03BA\u03C6\u03C1\u03AC\u03B6\u03B5\u03B9 \u03CC\u03C4\u03B9: \u0394\u03B5\u03BD \u03C5\u03C0\u03AC\u03C1\u03C7\u03B5\u03B9 \u03C3\u03CD\u03BD\u03BF\u03BB\u03BF \u03C4\u03BF\u03C5 \u03BF\u03C0\u03BF\u03AF\u03BF\u03C5 \u03B7 \u03C0\u03BB\u03B7\u03B8\u03B9\u03BA\u03CC\u03C4\u03B7\u03C4\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B1\u03C5\u03C3\u03C4\u03B7\u03C1\u03AC \u03B1\u03BD\u03AC\u03BC\u03B5\u03C3\u03B1 \u03C3\u03C4\u03B9\u03C2 \u03C0\u03BB\u03B7\u03B8\u03B9\u03BA\u03CC\u03C4\u03B7\u03C4\u03B5\u03C2 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03CC\u03BB\u03BF\u03C5 \u03C4\u03C9\u03BD \u03B1\u03BA\u03B5\u03C1\u03B1\u03AF\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03BA\u03B1\u03B9 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03CC\u03BB\u03BF\u03C5 \u03C4\u03C9\u03BD \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CE\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD. \u0397 \u03BF\u03BD\u03BF\u03BC\u03B1\u03C3\u03AF\u03B1 \u03C4\u03B7\u03C2 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7\u03C2 \u03C0\u03C1\u03BF\u03AD\u03C1\u03C7\u03B5\u03C4\u03B1\u03B9 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u03CC\u03C1\u03BF \u03B3\u03B9\u03B1 \u03C4\u03BF\u03C5\u03C2 \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03BF\u03CD\u03C2 \u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03CD\u03C2."@el ,
"Kontinuumhypotesen \u00E4r ett m\u00E4ngdteoretiskt p\u00E5st\u00E5ende av Georg Cantor som bland annat har betydelse inom matematikfilosofin. Hypotesen \u00E4r att det inte existerar n\u00E5got kardinaltal som ligger mellan kardinaltalet f\u00F6r m\u00E4ngden av de hela talen, Alef-noll, och kardinaltalet f\u00F6r m\u00E4ngden av de reella talen, kontinuum."@sv ,
"\u041A\u043E\u043D\u0442\u0438\u0301\u043D\u0443\u0443\u043C-\u0433\u0438\u043F\u043E\u0301\u0442\u0435\u0437\u0430 (\u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0430, \u043F\u0435\u0440\u0432\u0430\u044F \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430) \u2014 \u0432\u044B\u0434\u0432\u0438\u043D\u0443\u0442\u043E\u0435 \u0432 1877 \u0433\u043E\u0434\u0443 \u0413\u0435\u043E\u0440\u0433\u043E\u043C \u041A\u0430\u043D\u0442\u043E\u0440\u043E\u043C \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u043E \u0442\u043E\u043C, \u0447\u0442\u043E \u043B\u044E\u0431\u043E\u0435 \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0435 \u043F\u043E\u0434\u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0430 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043B\u0438\u0431\u043E \u0441\u0447\u0451\u0442\u043D\u044B\u043C, \u043B\u0438\u0431\u043E \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0430\u043B\u044C\u043D\u044B\u043C. \u0414\u0440\u0443\u0433\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u0433\u0438\u043F\u043E\u0442\u0435\u0437\u0430 \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u0430\u0433\u0430\u0435\u0442, \u0447\u0442\u043E \u043C\u043E\u0449\u043D\u043E\u0441\u0442\u044C \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0430 \u2014 \u043D\u0430\u0438\u043C\u0435\u043D\u044C\u0448\u0430\u044F, \u043F\u0440\u0435\u0432\u043E\u0441\u0445\u043E\u0434\u044F\u0449\u0430\u044F \u043C\u043E\u0449\u043D\u043E\u0441\u0442\u044C \u0441\u0447\u0451\u0442\u043D\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430, \u0438 \u00AB\u043F\u0440\u043E\u043C\u0435\u0436\u0443\u0442\u043E\u0447\u043D\u044B\u0445\u00BB \u043C\u043E\u0449\u043D\u043E\u0441\u0442\u0435\u0439 \u043C\u0435\u0436\u0434\u0443 \u0441\u0447\u0435\u0442\u043D\u044B\u043C \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E\u043C \u0438 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u043E\u043C \u043D\u0435\u0442. \u0412 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u044D\u0442\u043E \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u043E\u0437\u043D\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043E \u0434\u043B\u044F \u043B\u044E\u0431\u043E\u0433\u043E \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0432\u0441\u0435\u0433\u0434\u0430 \u043C\u043E\u0436\u043D\u043E \u0443\u0441\u0442\u0430\u043D\u043E\u0432\u0438\u0442\u044C \u0432\u0437\u0430\u0438\u043C\u043D\u043E-\u043E\u0434\u043D\u043E\u0437\u043D\u0430\u0447\u043D\u043E\u0435 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0435 \u043B\u0438\u0431\u043E \u043C\u0435\u0436\u0434\u0443 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u043C\u0438 \u044D\u0442\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0438 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E\u043C \u0446\u0435\u043B\u044B\u0445 \u0447\u0438\u0441\u0435\u043B, \u043B\u0438\u0431\u043E \u043C\u0435\u0436\u0434\u0443 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u043C\u0438 \u044D\u0442\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0438 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E\u043C \u0432\u0441\u0435\u0445 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B."@ru ,
"In matematica, l'ipotesi del continuo \u00E8 un'ipotesi avanzata da Georg Cantor che riguarda le dimensioni possibili per gli insiemi infiniti. Cantor introdusse il concetto di cardinalit\u00E0 e di numero cardinale (che possiamo immaginare come una \"dimensione\" dell'insieme) per confrontare tra loro insiemi transfiniti, e dimostr\u00F2 l'esistenza di insiemi infiniti di cardinalit\u00E0 diversa, come ad esempio i numeri naturali e i numeri reali. L'ipotesi del continuo afferma che: Non esiste nessun insieme la cui cardinalit\u00E0 \u00E8 strettamente compresa fra quella dei numeri interi e quella dei numeri reali."@it ,
"A hip\u00F3tese do continuum \u00E9 uma conjectura proposta por Georg Cantor. Esta conjectura consiste no seguinte: N\u00E3o existe nenhum conjunto com cardinalidade maior que a do conjunto dos n\u00FAmeros inteiros e menor que a do conjunto dos n\u00FAmeros reais. Aqui mais elementos e menos elementos tem um sentido muito preciso (ver n\u00FAmero cardinal). Esta hip\u00F3tese foi o n\u00FAmero um dos 23 Problemas de Hilbert apresentados na confer\u00EAncia do Congresso Internacional de Matem\u00E1tica de 1900, o que levou a que fosse estudada profundamente durante o s\u00E9culo XX."@pt ,
"In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers and the real numbers, or equivalently, that any subset of the real numbers is finite, is countably infinite, or has the same cardinality as the real numbers. In Zermelo\u2013Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following equation in aleph numbers: , or even shorter with beth numbers: ."@en ,
"\uC9D1\uD569\uB860\uC5D0\uC11C \uC5F0\uC18D\uCCB4 \uAC00\uC124(\u9023\u7E8C\u9AD4\u5047\u8AAA, \uC601\uC5B4: continuum hypothesis, \uC57D\uC790 CH)\uC740 \uC2E4\uC218 \uC9D1\uD569\uC758 \uBAA8\uB4E0 \uBD80\uBD84 \uC9D1\uD569\uC740 \uAC00\uC0B0 \uC9D1\uD569\uC774\uAC70\uB098 \uC544\uB2C8\uBA74 \uC2E4\uC218 \uC9D1\uD569\uACFC \uD06C\uAE30\uAC00 \uAC19\uB2E4\uB294 \uBA85\uC81C\uC774\uB2E4. \uC9D1\uD569\uB860\uC758 \uD45C\uC900\uC801 \uACF5\uB9AC\uACC4\uB85C\uB294 \uC99D\uBA85\uD560 \uC218\uB3C4, \uBC18\uC99D\uD560 \uC218\uB3C4 \uC5C6\uB2E4."@ko ,
"\u041A\u043E\u043D\u0442\u0438\u0301\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0301\u0442\u0435\u0437\u0430 \u2014 \u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430, \u044F\u043A\u0443 \u0432\u0438\u0441\u0443\u043D\u0443\u0432 \u0413\u0435\u043E\u0440\u0433 \u041A\u0430\u043D\u0442\u043E\u0440 \u0443 1877 \u0456 \u0437\u0433\u043E\u0434\u043E\u043C \u0431\u0435\u0437\u0443\u0441\u043F\u0456\u0448\u043D\u043E \u043D\u0430\u043C\u0430\u0433\u0430\u0432\u0441\u044F \u0457\u0457 \u0434\u043E\u0432\u0435\u0441\u0442\u0438, \u043C\u043E\u0436\u043D\u0430 \u0441\u0444\u043E\u0440\u043C\u0443\u043B\u044E\u0432\u0430\u0442\u0438 \u0442\u0430\u043A\u0438\u043C \u0447\u0438\u043D\u043E\u043C: \u0411\u0443\u0434\u044C-\u044F\u043A\u0430 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0430 \u043F\u0456\u0434\u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0443 \u0454 \u0430\u0431\u043E \u0437\u043B\u0456\u0447\u0435\u043D\u043D\u043E\u044E, \u0430\u0431\u043E \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0430\u043B\u044C\u043D\u043E\u044E. \u041A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u0441\u0442\u0430\u043B\u0430 \u043F\u0435\u0440\u0448\u043E\u044E \u0437 \u0434\u0432\u0430\u0434\u0446\u044F\u0442\u0438 \u0442\u0440\u044C\u043E\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C, \u043F\u0440\u043E \u044F\u043A\u0456 \u0414\u0430\u0432\u0438\u0434 \u0413\u0456\u043B\u044C\u0431\u0435\u0440\u0442 \u0434\u043E\u043F\u043E\u0432\u0456\u0432 \u043D\u0430 II \u041C\u0456\u0436\u043D\u0430\u0440\u043E\u0434\u043D\u043E\u043C\u0443 \u041A\u043E\u043D\u0433\u0440\u0435\u0441\u0456 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0456\u0432 \u0432 \u041F\u0430\u0440\u0438\u0436\u0456 1900 \u0440\u043E\u043A\u0443. \u0422\u043E\u043C\u0443 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u0432\u0456\u0434\u043E\u043C\u0430 \u0442\u0430\u043A\u043E\u0436 \u044F\u043A \u043F\u0435\u0440\u0448\u0430 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0413\u0456\u043B\u044C\u0431\u0435\u0440\u0442\u0430."@uk ,
"Die Kontinuumshypothese wurde 1878 vom Mathematiker Georg Cantor aufgestellt und beinhaltet eine Vermutung \u00FCber die M\u00E4chtigkeit des Kontinuums, das hei\u00DFt der Menge der reellen Zahlen. Dieses Problem hat sich nach einer langen Geschichte, die bis in die 1960er Jahre hineinreicht, als nicht entscheidbar herausgestellt, das hei\u00DFt, die Axiome der Mengenlehre erlauben in dieser Frage keine Entscheidung."@de .
@prefix dcterms: .
@prefix dbc: .
dbr:Continuum_hypothesis dcterms:subject dbc:Infinity ,
,
dbc:Independence_results ,
,
dbc:Cardinal_numbers ,
dbc:Basic_concepts_in_infinite_set_theory ,
dbc:Hypotheses ;
dbo:abstract "Hypot\u00E9za kontinua (ozna\u010Dovan\u00E1 n\u011Bkdy jako CH (z anglick\u00E9ho Continuum Hypothesis)) je matematick\u00E9 tvrzen\u00ED formulovan\u00E9 poprv\u00E9 Georgem Cantorem v roce 1882. Toto tvrzen\u00ED se t\u00FDk\u00E1 ot\u00E1zky, zda existuje n\u011Bjak\u00E1 mno\u017Eina, jej\u00ED\u017E mohutnost je ost\u0159e mezi mohutnost\u00ED mno\u017Einy p\u0159irozen\u00FDch \u010D\u00EDsel a mohutnost\u00ED mno\u017Einy \u010D\u00EDsel re\u00E1ln\u00FDch (neboli kontinua), a odpov\u00EDd\u00E1 na ni z\u00E1porn\u011B."@cs ,
"En teoria de conjunts, la hip\u00F2tesi del continu (abreviada HC) \u00E9s una hip\u00F2tesi, proposada per Georg Cantor, sobre la cardinalitat del conjunt dels nombres reals (denominat continu per la recta real). Cantor introdu\u00ED el concepte de nombre cardinal per comparar la mida de conjunts infinits, demostrant el 1874 que el cardinal del conjunt dels enters \u00E9s estrictament inferior al dels nombres reals. El seg\u00FCent a preguntar-se \u00E9s si existeixen conjunts tals que la seva cardinalitat estigui estrictament inclosa entre els dos conjunts. La hip\u00F2tesi del continu diu: No existeixen conjunts la mida dels quals estigui compresa estrictament entre el dels enters i el dels nombres reals. Matem\u00E0ticament parlant, si el cardinal dels enters \u00E9s (\u00E0lef zero) i el cardinal dels nombres reals \u00E9s , la hip\u00F2tesi del continu afirma que: on |A| indica el cardinal d'A. Acceptant l'axioma d'elecci\u00F3, existeix un nombre cardinal , l'immediat superior a , sent la hip\u00F2tesi del continu equivalent a la igualtat"@ca ,
"\u041A\u043E\u043D\u0442\u0438\u0301\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0301\u0442\u0435\u0437\u0430 \u2014 \u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430, \u044F\u043A\u0443 \u0432\u0438\u0441\u0443\u043D\u0443\u0432 \u0413\u0435\u043E\u0440\u0433 \u041A\u0430\u043D\u0442\u043E\u0440 \u0443 1877 \u0456 \u0437\u0433\u043E\u0434\u043E\u043C \u0431\u0435\u0437\u0443\u0441\u043F\u0456\u0448\u043D\u043E \u043D\u0430\u043C\u0430\u0433\u0430\u0432\u0441\u044F \u0457\u0457 \u0434\u043E\u0432\u0435\u0441\u0442\u0438, \u043C\u043E\u0436\u043D\u0430 \u0441\u0444\u043E\u0440\u043C\u0443\u043B\u044E\u0432\u0430\u0442\u0438 \u0442\u0430\u043A\u0438\u043C \u0447\u0438\u043D\u043E\u043C: \u0411\u0443\u0434\u044C-\u044F\u043A\u0430 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0430 \u043F\u0456\u0434\u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0443 \u0454 \u0430\u0431\u043E \u0437\u043B\u0456\u0447\u0435\u043D\u043D\u043E\u044E, \u0430\u0431\u043E \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0430\u043B\u044C\u043D\u043E\u044E. \u041A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u0441\u0442\u0430\u043B\u0430 \u043F\u0435\u0440\u0448\u043E\u044E \u0437 \u0434\u0432\u0430\u0434\u0446\u044F\u0442\u0438 \u0442\u0440\u044C\u043E\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C, \u043F\u0440\u043E \u044F\u043A\u0456 \u0414\u0430\u0432\u0438\u0434 \u0413\u0456\u043B\u044C\u0431\u0435\u0440\u0442 \u0434\u043E\u043F\u043E\u0432\u0456\u0432 \u043D\u0430 II \u041C\u0456\u0436\u043D\u0430\u0440\u043E\u0434\u043D\u043E\u043C\u0443 \u041A\u043E\u043D\u0433\u0440\u0435\u0441\u0456 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0456\u0432 \u0432 \u041F\u0430\u0440\u0438\u0436\u0456 1900 \u0440\u043E\u043A\u0443. \u0422\u043E\u043C\u0443 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u0432\u0456\u0434\u043E\u043C\u0430 \u0442\u0430\u043A\u043E\u0436 \u044F\u043A \u043F\u0435\u0440\u0448\u0430 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0413\u0456\u043B\u044C\u0431\u0435\u0440\u0442\u0430. 1940 \u0440\u043E\u043A\u0443 \u041A\u0443\u0440\u0442 \u0413\u0435\u0434\u0435\u043B\u044C \u0434\u043E\u0432\u0456\u0432, \u0449\u043E \u0443 \u0441\u0438\u0441\u0442\u0435\u043C\u0456 \u0430\u043A\u0441\u0456\u043E\u043C \u0426\u0435\u0440\u043C\u0435\u043B\u043E\u2014\u0424\u0440\u0435\u043D\u043A\u0435\u043B\u044F \u0437 \u0430\u043A\u0441\u0456\u043E\u043C\u043E\u044E \u0432\u0438\u0431\u043E\u0440\u0443 (ZFC), \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0443 \u043D\u0435 \u043C\u043E\u0436\u043D\u0430 \u0441\u043F\u0440\u043E\u0441\u0442\u0443\u0432\u0430\u0442\u0438 (\u0437\u0430 \u043F\u0440\u0438\u043F\u0443\u0449\u0435\u043D\u043D\u044F \u043F\u0440\u043E \u043D\u0435\u0441\u0443\u043F\u0435\u0440\u0435\u0447\u043D\u0456\u0441\u0442\u044C ZFC); \u0430 1963 \u0440\u043E\u043A\u0443 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u044C\u043A\u0438\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A \u0434\u043E\u0432\u0456\u0432, \u0449\u043E \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0443 \u043D\u0435 \u043C\u043E\u0436\u043D\u0430 \u0434\u043E\u0432\u0435\u0441\u0442\u0438, \u0432\u0438\u0445\u043E\u0434\u044F\u0447\u0438 \u0437 \u0442\u0438\u0445 \u0436\u0435 \u0430\u043A\u0441\u0456\u043E\u043C (\u0442\u0430\u043A\u043E\u0436 \u0443 \u043F\u0440\u0438\u043F\u0443\u0449\u0435\u043D\u043D\u0456 \u043F\u0440\u043E \u043D\u0435\u0441\u0443\u043F\u0435\u0440\u0435\u0447\u043D\u0456\u0441\u0442\u044C ZFC). \u0422\u0430\u043A\u0438\u043C \u0447\u0438\u043D\u043E\u043C, \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u043D\u0435 \u0437\u0430\u043B\u0435\u0436\u0438\u0442\u044C \u0432\u0456\u0434 \u0430\u043A\u0441\u0456\u043E\u043C ZFC."@uk ,
"Hipoteza continuum (CH, ang. continuum hypothesis) \u2013 hipoteza teorii mnogo\u015Bci dotycz\u0105ca mocy zbior\u00F3w liczb naturalnych i liczb rzeczywistych. M\u00F3wi ona, \u017Ce pomi\u0119dzy nimi nie ma \u017Cadnej wielko\u015Bci po\u015Bredniej; innymi s\u0142owy \u2013 continuum to najmniejsza liczba nieprzeliczalna, co formu\u0142uje si\u0119 r\u00F3wnaniem: . Hipotez\u0119 t\u0119 sformu\u0142owa\u0142 w XIX wieku Georg Cantor; znalaz\u0142a si\u0119 ona w\u015Br\u00F3d problem\u00F3w Hilberta, jako pierwsza na li\u015Bcie. W XX wieku udowodniono, \u017Ce problem ten jest nierozstrzygalny dla standardowej teorii mnogo\u015Bci, tj. niezale\u017Cny od aksjomat\u00F3w Zermela-Fraenkla."@pl ,
"A hip\u00F3tese do continuum \u00E9 uma conjectura proposta por Georg Cantor. Esta conjectura consiste no seguinte: N\u00E3o existe nenhum conjunto com cardinalidade maior que a do conjunto dos n\u00FAmeros inteiros e menor que a do conjunto dos n\u00FAmeros reais. Aqui mais elementos e menos elementos tem um sentido muito preciso (ver n\u00FAmero cardinal). Esta hip\u00F3tese foi o n\u00FAmero um dos 23 Problemas de Hilbert apresentados na confer\u00EAncia do Congresso Internacional de Matem\u00E1tica de 1900, o que levou a que fosse estudada profundamente durante o s\u00E9culo XX."@pt ,
"In de verzamelingenleer, een deelgebied van de wiskunde, is de continu\u00FCmhypothese een door Georg Cantor in 1877 geponeerde hypothese over de mogelijke kardinaliteiten van oneindige verzamelingen. De hypothese luidt dat: Er bestaat geen verzameling, waarvan de kardinaliteit tussen de kardinaliteit van de gehele getallen en de kardinaliteit van de re\u00EBle getallen ligt. De continu\u00FCmhypothese stelt dat de kardinaliteit van de verzameling re\u00EBle getallen, het continu\u00FCm, het eerste overaftelbare kardinaalgetal is, oftewel het eerste kardinaalgetal groter dan de kardinaliteit van de natuurlijke getallen."@nl ,
"\u9023\u7E8C\u7D71\u5047\u8A2D\uFF08\u82F1\u8A9E\uFF1AContinuum hypothesis\uFF0C\u7C21\u7A31CH\uFF09\u662F\u6570\u5B66\u4E2D\u4E00\u500B\u731C\u60F3\uFF0C\u4E5F\u662F\u5E0C\u5C14\u4F2F\u7279\u768423\u4E2A\u95EE\u9898\u7684\u7B2C\u4E00\u984C\uFF0C\u7531\u5EB7\u6258\u5C14\u63D0\u51FA\uFF0C\u95DC\u65BC\u7121\u7AAE\u96C6\u7684\u53EF\u80FD\u5927\u5C0F\u3002\u5176\u70BA\uFF1A \u4E0D\u5B58\u5728\u4E00\u500B\u57FA\u6570\u7D55\u5C0D\u5927\u4E8E\u53EF\u6578\u96C6\u800C\u7D55\u5C0D\u5C0F\u4E8E\u5B9E\u6570\u96C6\u7684\u96C6\u5408\u3002 \u5EB7\u6258\u723E\u5F15\u5165\u4E86\u57FA\u6578\u7684\u6982\u5FF5\u4EE5\u6BD4\u8F03\u7121\u7AAE\u96C6\u9593\u7684\u5927\u5C0F\uFF0C\u4E5F\u8B49\u660E\u4E86\u6574\u6578\u96C6\u7684\u57FA\u6578\u7D55\u5C0D\u5C0F\u65BC\u5BE6\u96C6\u7684\u57FA\u6578\u3002\u5EB7\u6258\u723E\u4E5F\u5C31\u7D66\u51FA\u4E86\u9023\u7E8C\u7D71\u5047\u8A2D\uFF0C\u5C31\u662F\u8BF4\uFF0C\u5728\u65E0\u9650\u96C6\u4E2D\uFF0C\u6BD4\u81EA\u7136\u6570\u96C6\u57FA\u6570\u5927\u7684\u96C6\u5408\u4E2D\uFF0C\u57FA\u6570\u6700\u5C0F\u7684\u96C6\u5408\u662F\u5B9E\u6570\u96C6\u3002\u800C\u9023\u7E8C\u7D71\u5C31\u662F\u5BE6\u6578\u96C6\u7684\u4E00\u500B\u820A\u7A31\u3002 \u66F4\u52A0\u5F62\u5F0F\u5730\u8BF4\uFF0C\u81EA\u7136\u6570\u96C6\u7684\u57FA\u6570\u4E3A\uFF08\u8B80\u4F5C\u300C\u963F\u5217\u592B\u96F6\u300D\uFF09\u3002\u800C\u8FDE\u7EED\u7EDF\u5047\u8BBE\u7684\u89C2\u70B9\u8BA4\u4E3A\u5B9E\u6570\u96C6\u7684\u57FA\u6570\u4E3A\uFF08\u8B80\u4F5C\u300C\u963F\u5217\u592B\u58F9\u300D\uFF09\u3002\u4E8E\u662F\uFF0C\u5EB7\u6258\u5C14\u5B9A\u4E49\u4E86\u7EDD\u5BF9\u65E0\u9650\u3002 \u7B49\u50F9\u5730\uFF0C\u6574\u6578\u96C6\u7684\u57FA\u6570\u662F\u800C\u5BE6\u6578\u7684\u57FA\u6570\u662F\uFF0C\u9023\u7E8C\u7D71\u5047\u8A2D\u6307\u51FA\u4E0D\u5B58\u5728\u4E00\u500B\u96C6\u5408\u4F7F\u5F97 \u5047\u8A2D\u9078\u64C7\u516C\u7406\u662F\u5C0D\u7684\uFF0C\u90A3\u5C31\u6703\u6709\u4E00\u500B\u6700\u5C0F\u7684\u57FA\u6578\u5927\u65BC\uFF0C\u800C\u9023\u7E8C\u7D71\u5047\u8A2D\u4E5F\u5C31\u7B49\u50F9\u65BC\u4EE5\u4E0B\u7684\u7B49\u5F0F\uFF1A \u9023\u7E8C\u7D71\u5047\u8A2D\u6709\u500B\u66F4\u5EE3\u7FA9\u7684\u5F62\u5F0F\uFF0C\u53EB\u4F5C\u5EE3\u7FA9\u9023\u7E8C\u7D71\u5047\u8A2D\uFF08GCH\uFF09\uFF0C\u5176\u547D\u984C\u70BA\uFF1A \u5BF9\u4E8E\u6240\u6709\u7684\u5E8F\u6570, \u5EAB\u723E\u7279\u00B7\u54E5\u5FB7\u5C14\u57281940\u5E74\u7528\u5185\u6A21\u578B\u6CD5\u8BC1\u660E\u4E86\u8FDE\u7EED\u7EDF\u5047\u8BBE\u4E0EZFC\u7684\u76F8\u5BF9\u534F\u8C03\u6027\uFF08\u7121\u6CD5\u4EE5ZFC\u8B49\u660E\u70BA\u8AA4\uFF09\uFF0C\u4FDD\u7F85\u00B7\u67EF\u6069\u57281963\u5E74\u7528\u529B\u8FEB\u6CD5\u8BC1\u660E\u4E86\u8FDE\u7EED\u7EDF\u5047\u8BBE\u4E0D\u80FD\u7531ZFC\u63A8\u5BFC\u3002\u4E5F\u5C31\u662F\u8BF4\u8FDE\u7EED\u7EDF\u5047\u8BBE\u65BCZFC\u3002"@zh ,
"Kontinuumhypotesen \u00E4r ett m\u00E4ngdteoretiskt p\u00E5st\u00E5ende av Georg Cantor som bland annat har betydelse inom matematikfilosofin. Hypotesen \u00E4r att det inte existerar n\u00E5got kardinaltal som ligger mellan kardinaltalet f\u00F6r m\u00E4ngden av de hela talen, Alef-noll, och kardinaltalet f\u00F6r m\u00E4ngden av de reella talen, kontinuum. Kurt G\u00F6del bevisade med hj\u00E4lp av att antagandet att kontinuumhypotesen \u00E4r sann inte strider mot m\u00E4ngdl\u00E4rans axiom i systemet ZFC. Emellertid visade matematikern genom att introducera metoden forcing \u00E5r 1963 att inte heller antagandet att kontinuumhypotesen \u00E4r falsk strider mot axiomen i ZFC. Det \u00E4r allts\u00E5 likgiltigt f\u00F6r m\u00E4ngdl\u00E4ran huruvida ett s\u00E5dant kardinaltal existerar eller inte, man kan inte avg\u00F6ra med dess hj\u00E4lp huruvida det finns eller inte. Att kontinuumhypotesen \u00E4r oavg\u00F6rbar inneb\u00E4r, enligt dem som f\u00F6respr\u00E5kar matematisk realism, att axiomsystemet ZFC inte beskriver den matematiska verkligheten tillr\u00E4ckligt precist f\u00F6r att kontinuumhypotesens verkliga sanningsv\u00E4rde skall kunna avg\u00F6ras. Andra realister h\u00E4vdar att det kan existera parallella m\u00E4ngdteoretiska universa: vissa d\u00E4r kontinuumhypotesen \u00E4r sann och andra d\u00E4r den \u00E4r falsk. Om man \u00E4r formalist tolkar man i st\u00E4llet resultatet bara som en matematisk egenskap hos ZFC som formellt system. Ett f\u00E5tal nutida m\u00E4ngdteoretiker, framf\u00F6rallt , anser att en djupare f\u00F6rst\u00E5else av m\u00E4ngdl\u00E4ran kan leda till insikter som f\u00E5r oss att acceptera nya axiom som skulle kunna avg\u00F6ra kontinuumhypotesen. Bland s\u00E5dana \u00E4r tendensen numera snarare att tro att kontinuumhypotesen \u00E4r falsk \u00E4n att den \u00E4r sann."@sv ,
"\u9023\u7D9A\u4F53\u4EEE\u8AAC\uFF08\u308C\u3093\u305E\u304F\u305F\u3044\u304B\u305B\u3064\u3001Continuum hypothesis, CH\uFF09\u3068\u306F\u3001\u53EF\u7B97\u6FC3\u5EA6\u3068\u9023\u7D9A\u4F53\u6FC3\u5EA6\u306E\u9593\u306B\u306F\u4ED6\u306E\u6FC3\u5EA6\u304C\u5B58\u5728\u3057\u306A\u3044\u3068\u3059\u308B\u4EEE\u8AAC\u300219\u4E16\u7D00\u306B\u30B2\u30AA\u30EB\u30AF\u30FB\u30AB\u30F3\u30C8\u30FC\u30EB\u306B\u3088\u3063\u3066\u63D0\u5531\u3055\u308C\u305F\u3002\u73FE\u5728\u306E\u6570\u5B66\u3067\u7528\u3044\u3089\u308C\u308B\u6A19\u6E96\u7684\u306A\u67A0\u7D44\u307F\u306E\u3082\u3068\u3067\u306F\u300C\u9023\u7D9A\u4F53\u4EEE\u8AAC\u306F\u8A3C\u660E\u3082\u53CD\u8A3C\u3082\u3067\u304D\u306A\u3044\u547D\u984C\u3067\u3042\u308B\u300D\u3068\u3044\u3046\u3053\u3068\u304C\u660E\u78BA\u306B\u8A3C\u660E\u3055\u308C\u3066\u3044\u308B\u3002"@ja ,
"\u0641\u0631\u0636\u064A\u0629 \u0627\u0644\u0627\u062A\u0635\u0627\u0644\u064A\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: continuum hypothesis)\u200F \u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0648\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u062D\u062F\u0633\u064A\u0629 \u0627\u0644\u0627\u062A\u0635\u0627\u0644\u064A\u0629 \u0648\u062A\u062E\u062A\u0635\u0631 CH\u060C \u0647\u064A \u062A\u0635\u0648\u0631 \u0648\u0636\u0639\u0647 \u0627\u0644\u0631\u064A\u0627\u0636\u064A \u062C\u0648\u0631\u062C \u0643\u0627\u0646\u062A\u0648\u0631 \u0639\u0627\u0645 1878\u0639\u0646 \u0627\u0644\u0623\u062D\u062C\u0627\u0645 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0644\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064A\u0629. \u0648\u062A\u0646\u0635 \u0639\u0644\u0649: (\u0644\u0627 \u064A\u0648\u062C\u062F \u0645\u062C\u0645\u0648\u0639\u0629 \u0639\u062F\u062F \u0639\u0646\u0627\u0635\u0631\u0647\u0627 \u0627\u0644\u0623\u0635\u0644\u064A\u0629 \u0645\u062D\u062F\u062F\u0629 \u0628\u0634\u0643\u0644 \u0635\u0627\u0631\u0645 \u0628\u064A\u0646 \u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u0635\u062D\u064A\u062D\u0629 \u0648\u0627\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u062D\u0642\u064A\u0642\u064A\u0629). \u0625\u0646 \u062D\u062F\u0633\u064A\u0629 \u0627\u0644\u0627\u062A\u0635\u0627\u0644\u064A\u0629 \u0644\u0643\u0627\u0646\u062A\u0648\u0631 \u0647\u064A \u0628\u0628\u0633\u0627\u0637\u0629 \u0627\u0644\u062A\u0633\u0627\u0624\u0644: \u0643\u0645 \u0639\u062F\u062F \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u0645\u0648\u062C\u0648\u062F\u0629 \u0639\u0644\u0649 \u062E\u0637 \u0645\u0633\u062A\u0642\u064A\u0645 \u0641\u064A \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0625\u0642\u0644\u064A\u062F\u064A\u061F \u0623\u0648 \u0628\u0635\u064A\u063A\u0629 \u0623\u062E\u0631\u0649: \u0643\u0645 \u0639\u062F\u062F \u0627\u0644\u0645\u062C\u0645\u0648\u0639\u0627\u062A \u0627\u0644\u0645\u062E\u062A\u0644\u0641\u0629 \u0627\u0644\u0645\u0648\u062C\u0648\u062F\u0629 \u0644\u0644\u0623\u0639\u062F\u0627\u062F \u0627\u0644\u0635\u062D\u064A\u062D\u0629\u061F \u0641\u0647\u064A \u062A\u0633\u0627\u0624\u0644 \u0639\u0646 \u0645\u0642\u062F\u0627\u0631 \u0623\u0648 \u062D\u062C\u0645 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064A\u0629."@ar ,
"In matematica, l'ipotesi del continuo \u00E8 un'ipotesi avanzata da Georg Cantor che riguarda le dimensioni possibili per gli insiemi infiniti. Cantor introdusse il concetto di cardinalit\u00E0 e di numero cardinale (che possiamo immaginare come una \"dimensione\" dell'insieme) per confrontare tra loro insiemi transfiniti, e dimostr\u00F2 l'esistenza di insiemi infiniti di cardinalit\u00E0 diversa, come ad esempio i numeri naturali e i numeri reali. L'ipotesi del continuo afferma che: Non esiste nessun insieme la cui cardinalit\u00E0 \u00E8 strettamente compresa fra quella dei numeri interi e quella dei numeri reali. Matematicamente parlando, dato che la cardinalit\u00E0 degli interi \u00E8 (aleph-zero) e la cardinalit\u00E0 dei numeri reali \u00E8 , l'ipotesi del continuo afferma: dove indica la cardinalit\u00E0 di . Il nome di questa ipotesi deriva dalla retta dei numeri reali, chiamata appunto \"il continuo\". Vi \u00E8 anche una generalizzazione dell'ipotesi del continuo, denominata \"ipotesi generalizzata del continuo\", e che afferma che per ogni cardinale transfinito T Gli studi di G\u00F6del e Cohen hanno permesso di stabilire che nella teoria degli insiemi di Zermelo - Fraenkel comprensiva dell'assioma di scelta l'ipotesi del continuo risulta indecidibile."@it ,
"\u041A\u043E\u043D\u0442\u0438\u0301\u043D\u0443\u0443\u043C-\u0433\u0438\u043F\u043E\u0301\u0442\u0435\u0437\u0430 (\u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0430, \u043F\u0435\u0440\u0432\u0430\u044F \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430) \u2014 \u0432\u044B\u0434\u0432\u0438\u043D\u0443\u0442\u043E\u0435 \u0432 1877 \u0433\u043E\u0434\u0443 \u0413\u0435\u043E\u0440\u0433\u043E\u043C \u041A\u0430\u043D\u0442\u043E\u0440\u043E\u043C \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u043E \u0442\u043E\u043C, \u0447\u0442\u043E \u043B\u044E\u0431\u043E\u0435 \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0435 \u043F\u043E\u0434\u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0430 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043B\u0438\u0431\u043E \u0441\u0447\u0451\u0442\u043D\u044B\u043C, \u043B\u0438\u0431\u043E \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0430\u043B\u044C\u043D\u044B\u043C. \u0414\u0440\u0443\u0433\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u0433\u0438\u043F\u043E\u0442\u0435\u0437\u0430 \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u0430\u0433\u0430\u0435\u0442, \u0447\u0442\u043E \u043C\u043E\u0449\u043D\u043E\u0441\u0442\u044C \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u0430 \u2014 \u043D\u0430\u0438\u043C\u0435\u043D\u044C\u0448\u0430\u044F, \u043F\u0440\u0435\u0432\u043E\u0441\u0445\u043E\u0434\u044F\u0449\u0430\u044F \u043C\u043E\u0449\u043D\u043E\u0441\u0442\u044C \u0441\u0447\u0451\u0442\u043D\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430, \u0438 \u00AB\u043F\u0440\u043E\u043C\u0435\u0436\u0443\u0442\u043E\u0447\u043D\u044B\u0445\u00BB \u043C\u043E\u0449\u043D\u043E\u0441\u0442\u0435\u0439 \u043C\u0435\u0436\u0434\u0443 \u0441\u0447\u0435\u0442\u043D\u044B\u043C \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E\u043C \u0438 \u043A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C\u043E\u043C \u043D\u0435\u0442. \u0412 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u044D\u0442\u043E \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u043E\u0437\u043D\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043E \u0434\u043B\u044F \u043B\u044E\u0431\u043E\u0433\u043E \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0432\u0441\u0435\u0433\u0434\u0430 \u043C\u043E\u0436\u043D\u043E \u0443\u0441\u0442\u0430\u043D\u043E\u0432\u0438\u0442\u044C \u0432\u0437\u0430\u0438\u043C\u043D\u043E-\u043E\u0434\u043D\u043E\u0437\u043D\u0430\u0447\u043D\u043E\u0435 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0435 \u043B\u0438\u0431\u043E \u043C\u0435\u0436\u0434\u0443 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u043C\u0438 \u044D\u0442\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0438 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E\u043C \u0446\u0435\u043B\u044B\u0445 \u0447\u0438\u0441\u0435\u043B, \u043B\u0438\u0431\u043E \u043C\u0435\u0436\u0434\u0443 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430\u043C\u0438 \u044D\u0442\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0438 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E\u043C \u0432\u0441\u0435\u0445 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B. \u041F\u0435\u0440\u0432\u044B\u0435 \u043F\u043E\u043F\u044B\u0442\u043A\u0438 \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u0430 \u044D\u0442\u043E\u0433\u043E \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043D\u0438\u044F \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430\u043C\u0438 \u043D\u0430\u0438\u0432\u043D\u043E\u0439 \u0442\u0435\u043E\u0440\u0438\u0438 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432 \u043D\u0435 \u0443\u0432\u0435\u043D\u0447\u0430\u043B\u0438\u0441\u044C \u0443\u0441\u043F\u0435\u0445\u043E\u043C, \u0432 \u0434\u0430\u043B\u044C\u043D\u0435\u0439\u0448\u0435\u043C \u043F\u043E\u043A\u0430\u0437\u0430\u043D\u0430 \u043D\u0435\u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E\u0441\u0442\u044C \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u044C \u0438\u043B\u0438 \u043E\u043F\u0440\u043E\u0432\u0435\u0440\u0433\u043D\u0443\u0442\u044C \u0433\u0438\u043F\u043E\u0442\u0435\u0437\u0443 \u0432 \u0430\u043A\u0441\u0438\u043E\u043C\u0430\u0442\u0438\u043A\u0435 \u0426\u0435\u0440\u043C\u0435\u043B\u043E \u2014 \u0424\u0440\u0435\u043D\u043A\u0435\u043B\u044F (\u043A\u0430\u043A \u0441 \u0430\u043A\u0441\u0438\u043E\u043C\u043E\u0439 \u0432\u044B\u0431\u043E\u0440\u0430, \u0442\u0430\u043A \u0438 \u0431\u0435\u0437 \u043D\u0435\u0451). \u041A\u043E\u043D\u0442\u0438\u043D\u0443\u0443\u043C-\u0433\u0438\u043F\u043E\u0442\u0435\u0437\u0430 \u043E\u0434\u043D\u043E\u0437\u043D\u0430\u0447\u043D\u043E \u0434\u043E\u043A\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0432 \u0441\u0438\u0441\u0442\u0435\u043C\u0435 \u0426\u0435\u0440\u043C\u0435\u043B\u043E \u2014 \u0424\u0440\u0435\u043D\u043A\u0435\u043B\u044F \u0441 \u0430\u043A\u0441\u0438\u043E\u043C\u043E\u0439 \u0434\u0435\u0442\u0435\u0440\u043C\u0438\u043D\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u043E\u0441\u0442\u0438 (ZF+AD)."@ru ,
"\uC9D1\uD569\uB860\uC5D0\uC11C \uC5F0\uC18D\uCCB4 \uAC00\uC124(\u9023\u7E8C\u9AD4\u5047\u8AAA, \uC601\uC5B4: continuum hypothesis, \uC57D\uC790 CH)\uC740 \uC2E4\uC218 \uC9D1\uD569\uC758 \uBAA8\uB4E0 \uBD80\uBD84 \uC9D1\uD569\uC740 \uAC00\uC0B0 \uC9D1\uD569\uC774\uAC70\uB098 \uC544\uB2C8\uBA74 \uC2E4\uC218 \uC9D1\uD569\uACFC \uD06C\uAE30\uAC00 \uAC19\uB2E4\uB294 \uBA85\uC81C\uC774\uB2E4. \uC9D1\uD569\uB860\uC758 \uD45C\uC900\uC801 \uACF5\uB9AC\uACC4\uB85C\uB294 \uC99D\uBA85\uD560 \uC218\uB3C4, \uBC18\uC99D\uD560 \uC218\uB3C4 \uC5C6\uB2E4."@ko ,
"In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers and the real numbers, or equivalently, that any subset of the real numbers is finite, is countably infinite, or has the same cardinality as the real numbers. In Zermelo\u2013Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following equation in aleph numbers: , or even shorter with beth numbers: . The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. The answer to this problem is independent of ZFC, so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt G\u00F6del in 1940. The name of the hypothesis comes from the term the continuum for the real numbers."@en ,
"En th\u00E9orie des ensembles, l'hypoth\u00E8se du continu (HC), due \u00E0 Georg Cantor, affirme qu'il n'existe aucun ensemble dont le cardinal est strictement compris entre le cardinal de l'ensemble des entiers naturels et celui de l'ensemble des nombres r\u00E9els. En d'autres termes : tout ensemble strictement plus grand, au sens de la cardinalit\u00E9, que l'ensemble des entiers naturels doit contenir une \u00AB copie \u00BB de l'ensemble des nombres r\u00E9els."@fr ,
"\u03A3\u03C4\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC, \u03B7 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03B5\u03C7\u03BF\u03CD\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B1 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7 \u03C3\u03C7\u03B5\u03C4\u03B9\u03BA\u03AC \u03BC\u03B5 \u03C4\u03B1 \u03C0\u03B9\u03B8\u03B1\u03BD\u03AC \u03BC\u03B5\u03B3\u03AD\u03B8\u03B7 \u03C4\u03C9\u03BD \u03B1\u03C0\u03B5\u03AF\u03C1\u03C9\u03BD \u03C3\u03CD\u03BD\u03BF\u03BB\u03C9\u03BD. \u0395\u03BA\u03C6\u03C1\u03AC\u03B6\u03B5\u03B9 \u03CC\u03C4\u03B9: \u0394\u03B5\u03BD \u03C5\u03C0\u03AC\u03C1\u03C7\u03B5\u03B9 \u03C3\u03CD\u03BD\u03BF\u03BB\u03BF \u03C4\u03BF\u03C5 \u03BF\u03C0\u03BF\u03AF\u03BF\u03C5 \u03B7 \u03C0\u03BB\u03B7\u03B8\u03B9\u03BA\u03CC\u03C4\u03B7\u03C4\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B1\u03C5\u03C3\u03C4\u03B7\u03C1\u03AC \u03B1\u03BD\u03AC\u03BC\u03B5\u03C3\u03B1 \u03C3\u03C4\u03B9\u03C2 \u03C0\u03BB\u03B7\u03B8\u03B9\u03BA\u03CC\u03C4\u03B7\u03C4\u03B5\u03C2 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03CC\u03BB\u03BF\u03C5 \u03C4\u03C9\u03BD \u03B1\u03BA\u03B5\u03C1\u03B1\u03AF\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03BA\u03B1\u03B9 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03CC\u03BB\u03BF\u03C5 \u03C4\u03C9\u03BD \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CE\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD. \u0397 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03B5\u03C7\u03BF\u03CD\u03C2 \u03B1\u03BD\u03B1\u03C0\u03C4\u03CD\u03C7\u03B8\u03B7\u03BA\u03B5 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u0393\u03BA\u03AD\u03BF\u03C1\u03B3\u03BA \u039A\u03AC\u03BD\u03C4\u03BF\u03C1 \u03C4\u03BF 1878, \u03BA\u03B1\u03B9 \u03B7 \u03B5\u03BE\u03B1\u03BA\u03C1\u03AF\u03B2\u03C9\u03C3\u03B7 \u03B3\u03B9\u03B1 \u03C4\u03BF \u03B1\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B1\u03BB\u03B7\u03B8\u03AE\u03C2 \u03AE \u03C8\u03B5\u03C5\u03B4\u03AE\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03BF \u03C0\u03C1\u03CE\u03C4\u03BF \u03B1\u03C0\u03CC \u03C4\u03B1 23 \u03C0\u03C1\u03BF\u03B2\u03BB\u03AE\u03BC\u03B1\u03C4\u03B1 \u03C4\u03BF\u03C5 \u03A7\u03AF\u03BB\u03BC\u03C0\u03B5\u03C1\u03C4, \u03C0\u03BF\u03C5 \u03C0\u03B1\u03C1\u03BF\u03C5\u03C3\u03B9\u03AC\u03C3\u03C4\u03B7\u03BA\u03B1\u03BD \u03C4\u03BF 1900. \u0397 \u03B1\u03C0\u03AC\u03BD\u03C4\u03B7\u03C3\u03B7 \u03C3\u03C4\u03BF \u03C0\u03C1\u03CC\u03B2\u03BB\u03B7\u03BC\u03B1 \u03B1\u03C5\u03C4\u03CC \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B1\u03BD\u03B5\u03BE\u03AC\u03C1\u03C4\u03B7\u03C4\u03B7 \u03B1\u03C0\u03CC \u03C4\u03B7 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C3\u03C5\u03BD\u03CC\u03BB\u03C9\u03BD \u03C4\u03C9\u03BD Zermelo-Fraenkel (\u03C3\u03C5\u03BC\u03C0\u03B5\u03C1\u03B9\u03BB\u03B1\u03BC\u03B2\u03B1\u03BD\u03BF\u03BC\u03AD\u03BD\u03BF\u03C5 \u03C4\u03BF\u03C5 \u03B1\u03BE\u03B9\u03CE\u03BC\u03B1\u03C4\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03B5\u03C0\u03B9\u03BB\u03BF\u03B3\u03AE\u03C2), \u03AD\u03C4\u03C3\u03B9 \u03CE\u03C3\u03C4\u03B5 \u03B5\u03AF\u03C4\u03B5 \u03B7 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7 \u03C4\u03BF\u03C5 \u03C3\u03C5\u03BD\u03B5\u03C7\u03BF\u03CD\u03C2 \u03B5\u03AF\u03C4\u03B5 \u03B7 \u03AC\u03C1\u03BD\u03B7\u03C3\u03AE \u03C4\u03B7\u03C2 \u03BC\u03C0\u03BF\u03C1\u03BF\u03CD\u03BD \u03BD\u03B1 \u03C0\u03C1\u03BF\u03C3\u03C4\u03B5\u03B8\u03BF\u03CD\u03BD \u03C9\u03C2 \u03B1\u03BE\u03AF\u03C9\u03BC\u03B1 \u03C3\u03C4\u03B7 (\u03B3\u03B9\u03B1 \u03C3\u03C5\u03BD\u03C4\u03BF\u03BC\u03AF\u03B1, \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C3\u03C5\u03BD\u03CC\u03BB\u03C9\u03BD ZFC), \u03BA\u03B1\u03B9 \u03B7 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C0\u03BF\u03C5 \u03C0\u03C1\u03BF\u03BA\u03CD\u03C0\u03C4\u03B5\u03B9 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BF\u03C1\u03B8\u03AE \u03B1\u03BD \u03BA\u03B1\u03B9 \u03BC\u03CC\u03BD\u03BF \u03B1\u03BD \u03B7 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C3\u03C5\u03BD\u03CC\u03BB\u03C9\u03BD ZFC \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BF\u03C1\u03B8\u03AE. \u0397 \u03B1\u03BD\u03B5\u03BE\u03B1\u03C1\u03C4\u03B7\u03C3\u03AF\u03B1 \u03B1\u03C5\u03C4\u03AE \u03B1\u03C0\u03BF\u03B4\u03B5\u03AF\u03C7\u03B8\u03B7\u03BA\u03B5 \u03C4\u03BF 1963 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD , \u03BF \u03BF\u03C0\u03BF\u03AF\u03BF\u03C2 \u03C3\u03C5\u03BC\u03C0\u03BB\u03AE\u03C1\u03C9\u03C3\u03B5 \u03AD\u03BD\u03B1 \u03C0\u03B1\u03BB\u03B1\u03B9\u03CC\u03C4\u03B5\u03C1\u03BF \u03AD\u03C1\u03B3\u03BF \u03C4\u03BF\u03C5 1940, \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u039A\u03BF\u03C5\u03C1\u03C4 \u0393\u03BA\u03AD\u03BD\u03C4\u03B5\u03BB. \u0397 \u03BF\u03BD\u03BF\u03BC\u03B1\u03C3\u03AF\u03B1 \u03C4\u03B7\u03C2 \u03C5\u03C0\u03CC\u03B8\u03B5\u03C3\u03B7\u03C2 \u03C0\u03C1\u03BF\u03AD\u03C1\u03C7\u03B5\u03C4\u03B1\u03B9 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD \u03CC\u03C1\u03BF \u03B3\u03B9\u03B1 \u03C4\u03BF\u03C5\u03C2 \u03C0\u03C1\u03B1\u03B3\u03BC\u03B1\u03C4\u03B9\u03BA\u03BF\u03CD\u03C2 \u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03CD\u03C2."@el ,
"Die Kontinuumshypothese wurde 1878 vom Mathematiker Georg Cantor aufgestellt und beinhaltet eine Vermutung \u00FCber die M\u00E4chtigkeit des Kontinuums, das hei\u00DFt der Menge der reellen Zahlen. Dieses Problem hat sich nach einer langen Geschichte, die bis in die 1960er Jahre hineinreicht, als nicht entscheidbar herausgestellt, das hei\u00DFt, die Axiome der Mengenlehre erlauben in dieser Frage keine Entscheidung."@de ,
"En teor\u00EDa de conjuntos, la hip\u00F3tesis del continuo (tambi\u00E9n conocida como primer problema de Hilbert) es un enunciado relativo a la cardinalidad del conjunto de los n\u00FAmeros reales, formulado como una hip\u00F3tesis por Georg Cantor en 1878. Su enunciado afirma que no existen conjuntos infinitos cuyo tama\u00F1o est\u00E9 estrictamente comprendido entre el del conjunto de los n\u00FAmeros naturales y el del conjunto de los reales. El nombre continuo hace referencia al conjunto de los reales. La hip\u00F3tesis del continuo fue uno de los 23 problemas de Hilbert propuestos en 1900. Las contribuciones de Kurt G\u00F6del y Paul Cohen demostraron que es de hecho independiente de los axiomas de Zermelo-Fraenkel, el conjunto de axiomas est\u00E1ndar en teor\u00EDa de conjuntos."@es ,
"En matematiko, la kontinua\u0135a hipotezo (iam mallonge CH) estas hipotezo pri la eblaj ampleksoj de malfiniaj aroj. \u011Ci asertas ke ne ekzistas aro kies kardinalo estas severe inter kardinalo de aro de entjeroj kaj kardinalo de aro de reelaj nombroj. La hipetezo estas de Georg Cantor de 1877. Kontrolado de vereco a\u016D malvereco de la kontinua\u0135a hipotezo estas la unua el la 23 prezentitaj en 1900. Laboroj de Kurt G\u00F6del en 1940 kaj en 1963 montris ke la hipotezo povas esti nek pruvita nek malpruvita uzante la aksiomojn de , la norma fundamento de moderna matematiko, se la aroteorio estas konsekvenca. La nomo de la hipotezo venas de la termino \"\" por la aro de reelaj nombroj."@eo ;
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