The Natural Numbers Are Well Ordered

Let $\mathbb{N}$ denote the natural numbers with the order $\le$, and let $A\subseteq\mathbb{N}$ be nonempty.

Then $A$ has a least element: there exists $a\in A$ such that $a\le m$ for every $m\in A$. This element is unique, and is denoted $\min A$.