Well-ordering

A well-ordering is a special kind of ordering

Definition

An ordering [math]<[/math] of a set [ilmath]P[/ilmath] which is both:

• Linear (total)
• strict

Is a well-ordering if every [ilmath]A\subset P[/ilmath] with [ilmath]A\ne\emptyset[/ilmath] has a least element. (Then [ilmath]A[/ilmath] is well-ordered)

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TODO: Finish off

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See also

• Well-ordered set