Solution
= Solution
A <bijection> between <finite sets> requires equal <cardinality>. When $m=n$, list the elements of $A$ and choose their distinct images in $n,n-1,\ldots,1$ ways. Thus
$$
\boxed{\#\{\text{bijections }A\to B\}=\begin{cases}n!&m=n,\\0&m\ne n.\end{cases}}
$$
The <factorial> convention $0!=1$ includes the unique <bijection> from the <empty set> to itself.