Identity Element of Natural Number Addition is Zero

From ProofWiki
Jump to navigation Jump to search

Theorem

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


Proof

Take the definition of natural numbers $\N$ as a naturally ordered semigroup $\left({\N, +, \le}\right)$.

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

$\blacksquare$