\begin{definition}[Definition:Finite Cardinal]
Let $\mathbf a$ be a cardinal.
Then $\mathbf a$ is described as '''finite''' {{iff}}:
:$\mathbf a < \mathbf a + \mathbf 1$
where $\mathbf 1$ is (cardinal) one.
That is, such that $\mathbf a \ne \mathbf a + \mathbf 1$.
\end{definition}