Definition:Set Equivalence

Definition
Two sets $S$ and $T$ are equivalent iff there is a bijection $f: S \to T$ between the elements of $S$ and those of $T$.

This can be written $S \sim T$.

Some sources use $S \simeq T$.

If $S$ and $T$ are not equivalent we write $S \not \sim T$.

Other terms that are used that mean the same things as equivalent are:
 * Equipotent (equalness of power), from which we refer to equivalent sets as having the same power
 * Equipollent (equalness of strength)
 * Equinumerous (equalness of number)
 * Similar.

Also see

 * Cardinality