# Ordinal Value Set

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An Ordinal Value Set is a value set of ordinal numbers that specified position of a sequence of numbers.

## References

### 2016

• (Wolfram Mathworld, 2016) ⇒ Weisstein, Eric W., Retrieved 2016-6-19 "Ordinal Number." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinalNumber.html
• In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc.

In formal set theory, an ordinal number (sometimes simply called an "ordinal" for short) is one of the numbers in Georg Cantor's extension of the whole numbers. An ordinal number is defined as the order type of a well ordered set (Dauben 1990, p. 199; Moore 1982, p. 52; Suppes 1972, p. 129). Finite ordinal numbers are commonly denoted using arabic numerals, while transfinite ordinals are denoted using lower case Greek letters.

It is easy to see that every finite totally ordered set is well ordered. Any two totally ordered sets with k elements (for k a nonnegative integer) are order isomorphic, and therefore have the same order type (which is also an ordinal number). The ordinals for finite sets are denoted 0, 1, 2, 3, ..., i.e., the integers one less than the corresponding nonnegative integers.