[lupire]

Nope.

Is the empty set countable? (Yes.)

Dictionary:

nat·u·ral num·bers

  the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well

Countable: https://en.wikipedia.org/wiki/Countable_set

Set theory:

https://en.wikipedia.org/wiki/Ordinal_number

[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.