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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.
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 .
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. [1] Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio.
In other words, every ordinal number α can be uniquely written as + + +, where k is a natural number, and … are ordinal numbers. Another variation of the Cantor normal form is the "base δ expansion", where ω is replaced by any ordinal δ > 1 , and the numbers c i are nonzero ordinals less than δ .
Since the epsilon numbers are an unbounded subclass of the ordinal numbers, they are enumerated using the ordinal numbers themselves. For any ordinal number , is the least epsilon number (fixed point of the exponential map) not already in the set {<}. It might appear that this is the non-constructive equivalent of the constructive definition ...
The nimber square of a Fermat 2-power x is equal to 3x/2 as evaluated under the ordinary multiplication of natural numbers. The smallest algebraically closed field of nimbers is the set of nimbers less than the ordinal ω ω ω , where ω is the smallest infinite ordinal.
The von Neumann cardinal assignment is a cardinal assignment that uses ordinal numbers. For a well-orderable set U , we define its cardinal number to be the smallest ordinal number equinumerous to U , using the von Neumann definition of an ordinal number.
This page was last edited on 29 February 2020, at 14:38 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
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