# 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.

$\blacksquare$