Proposition 1

A cardinal $\alpha$ is finite if and only if $\alpha + 1$ is finite.

For the relations $\alpha = \mathfrak{b}$ and $\alpha + 1 = \mathfrak{b} + 1$ between cardinals $\alpha$ and $\mathfrak{b}$ are equivalent (§ 3, no. 4, Proposition 8); the relations $\alpha \ne \alpha + 1$ and $\alpha + 1 \ne (\alpha + 1) + 1$ are therefore equivalent.

¶ It is clear that $0 \ne 1$; hence $0$ is an integer. It follows that $1$ and $2$ are integers. The cardinals $2 + 1$ and $(2 + 1) + 1$ are integers, denoted by $3$ and $4$, respectively.