totally ordered
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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
totally ordered set — noun A set having a specified total order … Wiktionary
Ordered group — In abstract algebra, an ordered group is a group (G,+) equipped with a partial order ≤ which 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 . Note that… … Wikipedia
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
Cyclically ordered group — In mathematics, a cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order. Cyclically ordered groups were first studied in depth by Ladislav Rieger… … 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
Linearly ordered group — In abstract algebra a linearly ordered or totally ordered group is an ordered group G such that the order relation le; is total. This means that the following statements hold for all a , b , c isin; G :* if a le; b and b le; a then a = b… … Wikipedia
Temporally-ordered routing algorithm — The Temporally Ordered Routing Algorithm (TORA) is an algorithm for routing data across Wireless Mesh Networks or Mobile ad hoc networks. It was developed by Vincent Park at the University of Maryland and the Naval Research Laboratory. Park has… … Wikipedia
