\begin{definition}[Definition:Set Equivalence]
Let $S$ and $T$ be sets.
Then $S$ and $T$ are '''equivalent''' {{iff}}:
:there exists a bijection $f: S \to T$ between the elements of $S$ and those of $T$.
That is, if they have the '''same cardinality'''.
This can be written $S \sim T$.
If $S$ and $T$ are not '''equivalent''' we write $S \nsim T$.
\end{definition}