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comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short)...40 KB (5,391 words) - 07:42, 25 August 2024
Weak ordering (redirect from Ordered partition of a set)orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders...30 KB (4,360 words) - 19:22, 2 February 2024- Order theory (section Partially ordered sets)b ≤ a then a = b (antisymmetry) if a ≤ b and b ≤ c then a ≤ c (transitivity). A set with a partial order on it is called a partially ordered set, poset...31 KB (4,508 words) - 03:55, 24 August 2024
- field of spectral graph theory. Dual to the observation above that every graph is an intersection graph is the fact that every partially ordered set (also...11 KB (1,209 words) - 11:19, 9 January 2024
- Lexicographic order (redirect from Lexicographically ordered)product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered. The words in a lexicon...23 KB (3,352 words) - 07:24, 16 November 2023
- of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable. The size of the...8 KB (1,090 words) - 11:19, 27 February 2023
- areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an antichain of incomparable...18 KB (2,429 words) - 18:50, 19 August 2024
specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named...22 KB (2,726 words) - 08:00, 11 January 2024
Hasse diagram (category Graphical concepts in set theory)theory, a Hasse diagram (/ˈhæsə/; German: [ˈhasə]) is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing...11 KB (1,336 words) - 08:49, 20 August 2024
Complete lattice (section Representation)In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A conditionally complete...18 KB (2,660 words) - 09:07, 2 September 2024- mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is...5 KB (715 words) - 14:47, 16 January 2024
- {\displaystyle C\succ A\iff C\succ B} (that is: the lower and upper contour sets of A and B are identical). He proved that, for every partially-ordered space ( X...19 KB (2,679 words) - 05:14, 26 July 2024
- Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in...21 KB (2,977 words) - 20:12, 17 July 2024
Monotonic function (category Pages that use a deprecated format of the math tags)In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...19 KB (2,467 words) - 04:06, 27 August 2024- ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract...13 KB (1,766 words) - 09:56, 30 January 2024
Filter (mathematics) (category Pages displaying wikidata descriptions as a fallback via Module:Annotated link)In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear...23 KB (2,809 words) - 10:19, 13 February 2024- ordered sets. Specifically, a filter on a set is just a proper order filter in the special case where the partially ordered set consists of the power set ordered...138 KB (23,299 words) - 13:29, 8 June 2024
- inequality, extreme value and mathematical optimization. Partially ordered set Preorder Totally ordered set Total preorder Chain Trichotomy Extended real number...5 KB (396 words) - 12:14, 30 October 2023
- mathematics, the order polytope of a finite partially ordered set is a convex polytope defined from the set. The points of the order polytope are the monotonic...9 KB (1,416 words) - 09:31, 17 December 2023
- Birkhoff's representation theorem, this lattice can be represented as the lower sets of an underlying partially ordered set. The elements of this set can be...26 KB (3,930 words) - 07:50, 19 January 2024
- Will and Representation by Arthur Schopenhauer, translated by R B Haldane and J. Kemp Second Book 143768The World as Will and Representation — Second
- consider a class of partially ordered sets called lattices; each of these corresponds to a distinct geometry. ... In the geometry of a topological space
- The set of playing cards is partially ordered, which means that sometimes you can compare cards and sometimes not. For example, you know that the 3 of Clubs