Definition:Smallest Natural Number

Definition
Let $S \subseteq \N$ be a subset of the natural numbers $\N$.

The smallest element $m$ of $S$ is defined as:
 * $\forall n \in S: m \le n$

That is, it is the minimal element of $S$ under the usual ordering.

Also see

 * Well-Ordering Principle: such an $m$ always exists