\begin{definition}[Definition:Comparable Sets/Cardinality]
Let $S$ and $T$ be sets.
Then $S$ and $T$ are '''comparable (in size)''' {{iff}} either:
:$S$ can be put into one-to-one correspondence with a subset of $T$
or:
:$T$ can be put into one-to-one correspondence with a subset of $S$
or both.
That is, if either $S$ is smaller than $T$ or $T$ is smaller than $S$.
\end{definition}