Natural numbers

The set of natural numbers, usually written \(\mathbb{N}\), sometimes includes 0 and sometimes doesn't include 0.

Relatedly, the set of integers \(\mathbb{Z}\) contains a subset \(\mathbb{Z}^+\). Sometimes this is used to mean strictly positive integers and so doesn't contain 0 and sometimes it is used to mean non-negative integers and does contain 0.

Sometimes authors define \(\mathbb{N}\) and \(\mathbb{Z}^+\) as the same thing, either with or without zero. Sometimes authors define them differently such that \(\mathbb{N}\) contains zero and \(\mathbb{Z}^+\) does not, and sometimes authors define them differently such that \(\mathbb{N}\) does not contain zero and \(\mathbb{Z}^+\) does.