ordinal number
ordinal number
English Definitions:
ordinal number, ordinal, no. (noun)
the number designating place in an ordered sequence
ordinal number (Noun)
A word that expresses the relative position of an item in an ordered sequence.
ordinal number (Noun)
A number used to denote position in a sequence.
ordinal number (Noun)
A generalized kind of number to denote the size of a well-ordered set.
Ordinal number
In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals. Like other kinds of numbers, ordinals can be added, multiplied, and exponentiated. Ordinals were introduced by Georg Cantor in 1883 to accommodate infinite sequences and to classify sets with certain kinds of order structures on them. He derived them by accident while working on a problem concerning trigonometric series—see Georg Cantor. Two sets S and S' have the same cardinality if there is a bijection between them If a partial order < is defined on set S, and a partial order <' is defined on set S', then the posets and are order isomorphic if there is a bijection f that preserves the ordering. That is, f <' f if and only if a < b. Every well ordered set is order isomorphic to the set of ordinals less than one specific ordinal number under their natural ordering.²³ωωε
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"ordinal number." Kamus.net. STANDS4 LLC, 2024. Web. 29 Apr. 2024. <https://www.kamus.net/english/ordinal+number>.
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