# Max Operation on Natural Numbers forms Monoid

## Theorem

Let $\left({\N, \max}\right)$ denote the algebraic structure formed from the natural numbers $\N$ and the max operation.

Then $\left({\N, \max}\right)$ is a monoid.

Its identity element is the zero.

## Proof

By the Well-Ordering Principle, $\N$ is a well-ordered set.

The result follows from Max Operation on Woset is Monoid.

$\blacksquare$