Theorem 1

The relation "$x$ is an integer" is collectivizing.

We shall denote by $\mathbf{N}$ the set of integers (also called "the set of natural integers" when necessary to avoid ambiguity). The cardinal of $\mathbf{N}$ is denoted by $\aleph_0$. Whenever $\mathbf{N}$ is considered as an ordered set, it is always the ordering (called the usual ordering) defined in § 3, no. 2 that is under consideration, unless the contrary is expressly stated.