cardinality

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the cardinality") is a type of number defined in such a way that any method of counting sets using it gives the same result. (This is not true for the ordinal numbers.) In fact, the cardinal numbers are obtained by collecting all ordinal numbers which are obtainable by counting a given set. A set has ℵ_0 (aleph-0) members if it can be put into a one-to-one correspondence with the finite ordinal numbers. The cardinality of a set is also frequently referred to as the "power" of a set.

aleph | aleph-0 | aleph-1 | Cantor-Dedekind axiom | Cantor diagonal method | cardinal addition | cardinal exponentiation | cardinal multiplication | continuum | continuum hypothesis | equipollent | inaccessible cardinal | infinity | ordinal number | power set | uncountably infinite