Definition:Finite Cardinal

Definition
Let $\mathbf a$ be a cardinal.

Then $\mathbf a$ is described as finite :
 * $\mathbf a < \mathbf a + \mathbf 1$

where $\mathbf 1$ is (cardinal) one.

That is, such that $\mathbf a \ne \mathbf a + \mathbf 1$.