Pic related is a true statement. If I wanted to talk about the set of positive whole numbers I'd just put
$\mathbb{Z}_+ = \{1, 2, 3, \dots\}$
like a normal person. The + means positive, schizos. 0 is not positive nor negative. Hence $0 \notin \mathbb{Z}$ and hence it would only make sense to have $0 \in \mathbb{N}$