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# totally ordered set

a set in which a relation, as "less than or equal to," holds for all pairs of elements of the set. Also called chain, linearly ordered set, simply ordered set. Cf. partially ordered set, well-ordered set.

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Universalium. 2010.

### Look at other dictionaries:

• totally ordered set — Math. a set in which a relation, as less than or equal to, holds for all pairs of elements of the set. Also called chain, linearly ordered set, simply ordered set. Cf. partially ordered set, well ordered set …   Useful english dictionary

• totally ordered set — noun A set having a specified total order …   Wiktionary

• Ordered set — In order theory in mathematics, a set with a binary relation R on its elements that is reflexive (for all a in the set, aRa), antisymmetric (if aRb and bRa, then a = b) and transitive (if aRb and bRc, then aRc) is described as a… …   Wikipedia

• Partially ordered set — The Hasse diagram of the set of all subsets of a three element set {x, y, z}, ordered by inclusion. In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering,… …   Wikipedia

• well-ordered set — Math. a totally ordered set in which every nonempty subset has a smallest element with the property that there is no element in the subset less than this smallest element. Cf. partially ordered set, totally ordered set. * * * …   Universalium

• well-ordered set — Math. a totally ordered set in which every nonempty subset has a smallest element with the property that there is no element in the subset less than this smallest element. Cf. partially ordered set, totally ordered set …   Useful english dictionary

• partially ordered set — Math. a set in which a relation as less than or equal to holds for some pairs of elements of the set, but not for all. Cf. totally ordered set, well ordered set. [1970 75] * * * …   Universalium

• partially ordered set — Math. a set in which a relation as less than or equal to holds for some pairs of elements of the set, but not for all. Cf. totally ordered set, well ordered set. [1970 75] …   Useful english dictionary

• linearly ordered set — Math. See totally ordered set. * * * …   Universalium

• simply ordered set — Math. See totally ordered set. * * * …   Universalium