Definition:Set Equivalence

Two sets $$S$$ and $$T$$ are equivalent iff there is a bijection between the elements of $$S$$ and those of $$T$$.

This can be written $$S \sim T$$.

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".