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.

$\blacksquare$


Sources

  • 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 8$: Compositions Induced on Subsets: Example $8.4$
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