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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. 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 ...

  4. Numeral prefix - Wikipedia

    en.wikipedia.org/wiki/Numeral_prefix

    The ordinal category are based on ordinal numbers such as the English first, second, third, which specify position of items in a sequence. In Latin and Greek, the ordinal forms are also used for fractions for amounts higher than 2; only the fraction ⁠ 1 / 2 ⁠ has special forms.

  5. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.

  6. Even and odd ordinals - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_ordinals

    Otherwise α = 2β + 1 and α is odd. [5] [6] Unlike the case of even integers, one cannot go on to characterize even ordinals as ordinal numbers of the form β2 = β + β. Ordinal multiplication is not commutative, so in general 2β ≠ β2. In fact, the even ordinal ω + 4 cannot be expressed as β + β, and the ordinal number

  7. Ordinal arithmetic - Wikipedia

    en.wikipedia.org/wiki/Ordinal_arithmetic

    The equation 2 ω = ω expresses the fact that finite sequences of zeros and ones can be identified with natural numbers, using the binary number system. The ordinal ω ω can be viewed as the order type of finite sequences of natural numbers; every element of ω ω (i.e. every ordinal smaller than ω ω) can be uniquely written in the form ...

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