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## Proposition: Well-Ordering Principle of Natural Numbers

The natural numbers together with their order relation $(\mathbb N,\le)$ is a well-ordered set, i.e. each non-empty subset $$M\subseteq\mathbb N$$ contains a unique smallest element $$m_0 \le m\in M$$.

### Strict order version:

The natural numbers together with their order relation $(\mathbb N, < )$ is a well-ordered set, i.e. each non-empty subset $$M\subseteq\mathbb N$$ contains a unique minimal element $$m_0 < m\in M$$.

| | | | | created: 2014-06-21 14:30:54 | modified: 2019-07-28 13:58:35 | by: bookofproofs | references: [696]