Identity Element of Natural Number Addition is Zero

Theorem
The identity element for the natural numbers under addition is zero ($0$):


 * $\forall n \in \N: 0 + n = n$

Proof
Take the definition of natural numbers $\N$ as a naturally ordered semigroup $\struct {\N, +, \le}$.

The result follows from Zero is Identity in Naturally Ordered Semigroup.