Category:Definitions/Set Equivalence

This category contains definitions related to Set Equivalence.
Related results can be found in Category:Set Equivalence.

Let $S$ and $T$ be sets.

Then $S$ and $T$ are equivalent if and only if:

there exists a bijection $f: S \to T$ between the elements of $S$ and those of $T$.

That is, if and only if they have the same cardinality.

This can be written $S \sim T$.

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