Two sets A and B are said to be equinumerous if they have the same cardinality, i.e., if there exists a bijectionf : A → B. This is denoted
The study of cardinality is often called equinumerosity. Sometimes the terms equipollent or even equivalent are used, though equivalent is a bit overused. More at cardinality.
It is thus said that two sets with the same cardinality are, respectively, equipotent, equipollent, or equinumerous.
Formally, assuming the axiom of choice, cardinality of a set X is the least ordinal α such that there is a bijection between X and α.
If the axiom of choice is not assumed and X does not have a well-ordering, the cardinality of X is defined to be the set of all sets which are equinumerous with X and have the least rank that a set equinumerous with X can have.
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