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  2. Ordinal number - Wikipedia

    en.wikipedia.org/wiki/Ordinal_number

    Cantor's work with derived sets and ordinal numbers led to the Cantor-Bendixson theorem. [14] Using successors, limits, and cardinality, Cantor generated an unbounded sequence of ordinal numbers and number classes. [15] The (α + 1)-th number class is the set of ordinals whose predecessors form a set of the same cardinality as the α-th

  3. Even and odd ordinals - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_ordinals

    In fact, the even ordinal ω + 4 cannot be expressed as β + β, and the ordinal number (ω + 3)2 = (ω + 3) + (ω + 3) = ω + (3 + ω) + 3 = ω + ω + 3 = ω2 + 3. is not even. A simple application of ordinal parity is the idempotence law for cardinal addition (given the well-ordering theorem). Given an infinite cardinal κ, or generally any ...

  4. Cardinal and Ordinal Numbers - Wikipedia

    en.wikipedia.org/wiki/Cardinal_and_Ordinal_Numbers

    Cardinal and Ordinal Numbers is a book on transfinite numbers, by Polish mathematician Wacław Sierpiński. It was published in 1958 by Państwowe Wydawnictwo Naukowe , as volume 34 of the series Monografie Matematyczne of the Institute of Mathematics of the Polish Academy of Sciences .

  5. First uncountable ordinal - Wikipedia

    en.wikipedia.org/wiki/First_uncountable_ordinal

    Any ordinal number can be turned into a topological space by using the order topology. When viewed as a topological space, ω 1 {\displaystyle \omega _{1}} is often written as [ 0 , ω 1 ) {\displaystyle [0,\omega _{1})} , to emphasize that it is the space consisting of all ordinals smaller than ω 1 {\displaystyle \omega _{1}} .

  6. Regular cardinal - Wikipedia

    en.wikipedia.org/wiki/Regular_cardinal

    An infinite ordinal is a regular ordinal if it is a limit ordinal that is not the limit of a set of smaller ordinals that as a set has order type less than . A regular ordinal is always an initial ordinal , though some initial ordinals are not regular, e.g., ω ω {\displaystyle \omega _{\omega }} (see the example below).

  7. Ordinal numeral - Wikipedia

    en.wikipedia.org/wiki/Ordinal_numeral

    Ordinal indicator – Character(s) following an ordinal number (used when writing ordinal numbers, such as a super-script) Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics; Ordinal date – Date written as number of days since first day of ...

  8. Transfinite number - Wikipedia

    en.wikipedia.org/wiki/Transfinite_number

    Any finite natural number can be used in at least two ways: as an ordinal and as a cardinal. Cardinal numbers specify the size of sets (e.g., a bag of five marbles), whereas ordinal numbers specify the order of a member within an ordered set [9] (e.g., "the third man from the left" or "the twenty-seventh day of January").

  9. Category:Ordinal numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Ordinal_numbers

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