◀ ▲ ▶Branches / Number-systems-arithmetics / Proposition: Well-Ordering Principle of Natural Numbers

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 \(m_0 < m\in M\).

Table of Contents

Proofs: 1

Mentioned in:

Definitions: 1 2
Proofs: 3 4 5 6 7 8 9 10 11 12 13
Propositions: 14

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

1. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013