Difference between revisions of "Well-ordering"
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| − | Is a ''well-ordering'' if every {{M|A\subset P}} with {{M|A\ne\emptyset}} has a least element. | + | Is a ''well-ordering'' if every {{M|A\subset P}} with {{M|A\ne\emptyset}} has a least element. (Then {{M|A}} is ''[[Well-ordered set|well-ordered]]''<ref name="Top">Topology - James R. Munkres - 2nd edition</ref>) |
{{Todo|Finish off}} | {{Todo|Finish off}} | ||
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| + | ==See also== | ||
| + | * [[Well-ordered set]] | ||
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| + | ==References== | ||
| + | <references/> | ||
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{{Definition|Set Theory}} | {{Definition|Set Theory}} | ||
Latest revision as of 17:34, 24 July 2015
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
