- well-ordering
- noun see well-ordered
New Collegiate Dictionary. 2001.
well-ordering
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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 — See ordering relation … Philosophy 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 — /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
