Definition 1

Tag 03JY, permanent. Cite it as [Bourbaki, Tag 03JY].

Theory of Sets, chapter III, § 2. Well-ordered sets

A set E is said to be well-ordered if it is ordered and if each non-empty subset of E has a least element.

A well-ordered set E is totally ordered because every subset $\{x, y\}$ of E has a least element. Every subset A of E which is bounded above in E has a least upper bound in E.

Examples

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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Cites

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