Definition:Smallest Natural Number
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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