Definition 3

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

Theory of Sets, chapter III, § 1. Order relations. Ordered sets

Let E be an ordered set. An element $a \in E$ is said to be a minimal (resp. maximal) element of E if the relation $x \leqslant a$ (resp. $x \geqslant a$ ) implies $x = a$ .

Every minimal element of E is a maximal element with respect to the opposite ordering, and vice versa.

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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