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In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets. [ 1 ] A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used.
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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 ...
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 ...
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.
A standard roulette wheel contains the number 0 as well as 1-36. It appears in green, so is classed as neither a "red" nor "black" number for betting purposes. The card game Uno has number cards running from 0 to 9 along with special cards, within each coloured suit. The Four Essential Freedoms of Free Software are numbered starting from zero ...
Any well-ordered set having that ordinal as its order type has the same cardinality. The smallest ordinal having a given cardinal as its cardinality is called the initial ordinal of that cardinal. Every finite ordinal (natural number) is initial, but most infinite ordinals are not initial.
In written languages, an ordinal indicator is a character, or group of characters, following a numeral denoting that it is an ordinal number, rather than a cardinal number. Historically these letters were "elevated terminals", that is to say the last few letters of the full word denoting the ordinal form of the number displayed as a superscript .