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]

1.Proof: (related to "Well-Ordering Principle of Natural Numbers")