Max Operation on Natural Numbers forms Monoid

Theorem
Let $\struct {\N, \max}$ denote the algebraic structure formed from the natural numbers $\N$ and the max operation.

Then $\struct {\N, \max}$ is a monoid.

Its identity element is zero.

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

The result follows from Max Operation on Woset is Monoid.