| 释义 |
ordinal number Informally, a number denoting the position in a sequence, so ‘first', ‘second', ‘third' is the start of the ordinal numbers, thus designating order as opposed to the cardinal numbers. More generally, in set theory, two well-ordered sets have the same ordinal number if they are order isomorphic. As with cardinal arithmetic, ordinal numbers can be added, multiplied, and exponentiated. The ordinal number of the natural numbers with the usual ordering is denoted ω. Perhaps surprisingly 1 + ω = ω, but ω + 1 ≠ ω, as the natural numbers do not have a largest element.
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