Natural Numbers are Non-Negative Integers

Theorem
Let $m \in \Z$. Then:


 * $(1): \quad m \in \N \iff 0 \le m$
 * $(2): \quad m \in \N_{> 0} \iff 0 < m$
 * $(3): \quad m \notin \N \iff -m \in \N_{> 0}$

That is, the natural numbers are precisely those integers which are greater than or equal to zero.