Natural_Numbers_are_Non_Negative_Integers

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.