- partially ordered set
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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]
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Universalium. 2010.
partially ordered set
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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
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
partially ordered set — noun a) A set having a specified partial order. b) Said set together with said partial order; the ordered pair of said set and said partial order. Syn: poset … 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
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. * * * … Universalium
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
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 group — In abstract algebra, a partially ordered group is a group (G,+) equipped with a partial order ≤ that is translation invariant; in other words, ≤ has the property that, for all a, b, and g in G, if a ≤ b then a+g ≤ b+g and g+a ≤ g+b. An element x… … Wikipedia
partially ordered — adjective Of a set, having a specified partial order; often construed with by … Wiktionary
