# well-ordering

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well-ordering

Philosophy dictionary. . 2011.

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• well-ordering — noun see well ordered …   New Collegiate Dictionary

• well-ordering — noun A total order of which every nonempty subset has a least element. Syn: well order …   Wiktionary

• well-ordering — ¦ ̷ ̷ ˈ ̷ ̷ ( ̷ ̷ ) ̷ ̷ noun ( s) : an instance of being well ordered …   Useful english dictionary

• Well-ordering theorem — The well ordering theorem (not to be confused with the well ordering axiom) states that every set can be well ordered.This is important because it makes every set susceptible to the powerful technique of transfinite induction.Georg Cantor… …   Wikipedia

• Well-ordering principle — In mathematics, the well ordering principle states that every non empty set of positive integers contains a smallest element. [cite book |title=Introduction to Analytic Number Theory |last=Apostol |first=Tom |authorlink=Tom M. Apostol |year=1976… …   Wikipedia

• well-ordering theorem — /wel awr deuhr ing/, Math. the theorem of set theory that every set can be made a well ordered set. * * * …   Universalium

• well-ordering theorem — /wel awr deuhr ing/, Math. the theorem of set theory that every set can be made a well ordered set …   Useful english dictionary

• Well-order — In mathematics, a well order relation (or well ordering) on a set S is a total order on S with the property that every non empty subset of S has a least element in this ordering.Equivalently, a well ordering is a well founded total order.The set… …   Wikipedia

• Well-founded relation — In mathematics, a binary relation, R, is well founded (or wellfounded) on a class X if and only if every non empty subset of X has a minimal element with respect to R; that is, for every non empty subset S of X, there is an element m of S such… …   Wikipedia

• ordering relation — A partial ordering on a set is a relation < that is transitive and reflexive and antisymmetric. That is, (i) x < y & y < z →x < z ; (ii) x < x ; (iii) x < y & y < x →x = y . If we add (iv) that at least one of x < y, x = y …   Philosophy dictionary

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