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- First_uncountable_ordinal abstract "In mathematics, the first uncountable ordinal, traditionally denoted by ω1 or sometimes by Ω, is the smallest ordinal number that, considered as a set, is uncountable. It is the supremum of all countable ordinals. The elements of ω1 are the countable ordinals, of which there are uncountably many.Like any ordinal number (in von Neumann's approach), ω1 is a well-ordered set, with set membership ("∈") serving as the order relation. ω1 is a limit ordinal, i.e. there is no ordinal α with α + 1 = ω1.The cardinality of the set ω1 is the first uncountable cardinal number, ℵ1 (aleph-one). The ordinal ω1 is thus the initial ordinal of ℵ1.Indeed, in most constructions ω1 and ℵ1 are equal as sets. To generalize: if α is an arbitrary ordinal we define ωα as the initial ordinal of the cardinal ℵα.The existence of ω1 can be proven without the axiom of choice. (See Hartogs number.)".
- First_uncountable_ordinal wikiPageID "20860540".
- First_uncountable_ordinal wikiPageLength "3030".
- First_uncountable_ordinal wikiPageOutDegree "26".
- First_uncountable_ordinal wikiPageRevisionID "663920033".
- First_uncountable_ordinal wikiPageWikiLink Aleph_number.
- First_uncountable_ordinal wikiPageWikiLink Axiom_of_choice.
- First_uncountable_ordinal wikiPageWikiLink Cardinal_number.
- First_uncountable_ordinal wikiPageWikiLink Cardinality.
- First_uncountable_ordinal wikiPageWikiLink Category:Ordinal_numbers.
- First_uncountable_ordinal wikiPageWikiLink Category:Topological_spaces.
- First_uncountable_ordinal wikiPageWikiLink Continuum_hypothesis.
- First_uncountable_ordinal wikiPageWikiLink Counterexamples_in_Topology.
- First_uncountable_ordinal wikiPageWikiLink Element_(mathematics).
- First_uncountable_ordinal wikiPageWikiLink Hartogs_number.
- First_uncountable_ordinal wikiPageWikiLink Infimum_and_supremum.
- First_uncountable_ordinal wikiPageWikiLink Large_countable_ordinal.
- First_uncountable_ordinal wikiPageWikiLink Limit_ordinal.
- First_uncountable_ordinal wikiPageWikiLink Long_line_(topology).
- First_uncountable_ordinal wikiPageWikiLink Mathematics.
- First_uncountable_ordinal wikiPageWikiLink Order_topology.
- First_uncountable_ordinal wikiPageWikiLink Ordinal_arithmetic.
- First_uncountable_ordinal wikiPageWikiLink Ordinal_number.
- First_uncountable_ordinal wikiPageWikiLink Sequence.
- First_uncountable_ordinal wikiPageWikiLink Set_(mathematics).
- First_uncountable_ordinal wikiPageWikiLink Set_membership.
- First_uncountable_ordinal wikiPageWikiLink Supremum.
- First_uncountable_ordinal wikiPageWikiLink Topological_space.
- First_uncountable_ordinal wikiPageWikiLink Topology.
- First_uncountable_ordinal wikiPageWikiLink Tychonoff_plank.
- First_uncountable_ordinal wikiPageWikiLink Uncountable.
- First_uncountable_ordinal wikiPageWikiLink Uncountable_set.
- First_uncountable_ordinal wikiPageWikiLink Well-order.
- First_uncountable_ordinal wikiPageWikiLinkText "First uncountable ordinal".
- First_uncountable_ordinal wikiPageWikiLinkText "first uncountable ordinal ".
- First_uncountable_ordinal wikiPageWikiLinkText "first uncountable ordinal number".
- First_uncountable_ordinal wikiPageWikiLinkText "first uncountable ordinal".
- First_uncountable_ordinal wikiPageWikiLinkText "omega-one".
- First_uncountable_ordinal hasPhotoCollection First_uncountable_ordinal.
- First_uncountable_ordinal subject Category:Ordinal_numbers.
- First_uncountable_ordinal subject Category:Topological_spaces.
- First_uncountable_ordinal hypernym Number.
- First_uncountable_ordinal type Space.
- First_uncountable_ordinal comment "In mathematics, the first uncountable ordinal, traditionally denoted by ω1 or sometimes by Ω, is the smallest ordinal number that, considered as a set, is uncountable. It is the supremum of all countable ordinals. The elements of ω1 are the countable ordinals, of which there are uncountably many.Like any ordinal number (in von Neumann's approach), ω1 is a well-ordered set, with set membership ("∈") serving as the order relation. ω1 is a limit ordinal, i.e.".
- First_uncountable_ordinal label "First uncountable ordinal".
- First_uncountable_ordinal sameAs Primer_ordinal_no_numerable.
- First_uncountable_ordinal sameAs Premier_ordinal_non_dénombrable.
- First_uncountable_ordinal sameAs 最小の非可算順序数.
- First_uncountable_ordinal sameAs m.0542phz.
- First_uncountable_ordinal sameAs Q3401770.
- First_uncountable_ordinal sameAs Q3401770.
- First_uncountable_ordinal wasDerivedFrom First_uncountable_ordinal?oldid=663920033.
- First_uncountable_ordinal isPrimaryTopicOf First_uncountable_ordinal.