# Well-ordering

From Maths

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*^{[1]})

TODO: Finish off

## See also

## References

- ↑ Topology - James R. Munkres - 2nd edition