[atwood22]

From your own link on countable sets:

> Equivalently, a set S is countable if there exists an injective function f : S → N from S to N; it simply means that every element in S corresponds to a different element in N.

Defining N is usually done via a successor set, on which case 0 makes no sense to include.

[lupire]

A successor set is the set of successors of... 0 or 1, depending on what you are doing.