# Equinumerosity

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Equinumerosity

In the field of mathematics, two sets "A" and "B" are equinumerous if they have the same cardinality, i.e., if there exists a bijection "f" : "A" → "B". This is usually denoted

:$A approx B ,$ or $A sim B$.

The study of cardinality is often called equinumerosity ("equalness-of-number"). The terms equipollence ("equalness-of-strength") and equipotence ("equalness-of-power") are sometimes used instead.

In Set, the category of all sets with functions as morphisms, an isomorphism between two sets is precisely a bijection, and two sets are equinumerous precisely if they are isomorphic in this category.

ee also

*Category of sets
*Cardinal number
*Cardinality
*Bijection

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