**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