antisymmetric set
51Supremum — In mathematics, given a subset S of a partially ordered set T , the supremum (sup) of S , if it exists, is the least element of T that is greater than or equal to each element of S . Consequently, the supremum is also referred to as the least… …
52Surreal number — In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share… …
53Total order — In set theory, a total order, linear order, simple order, or (non strict) ordering is a binary relation (here denoted by infix ≤) on some set X. The relation is transitive, antisymmetric, and total. A set paired with a total order is called a… …
54Forcing (mathematics) — For the use of forcing in recursion theory, see Forcing (recursion theory). In the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963,… …
55Mereology — In philosophy and mathematical logic, mereology (from the Greek μέρος, root: μερε(σ) , part and the suffix logy study, discussion, science ) treats parts and the wholes they form. Whereas set theory is founded on the membership relation between a …
56Closure operator — In mathematics, a closure operator on a set S is a function cl: P(S) → P(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S. X ⊆ cl(X) (cl is extensive) X ⊆ Y implies cl(X) ⊆ cl(Y)   (cl… …
57Dedekind–MacNeille completion — The Hasse diagram of a partially ordered set (left) and its Dedekind–MacNeille completion (right). In order theoretic mathematics, the Dedekind–MacNeille completion of a partially ordered set (also called the completion by cuts or normal… …
58Finitary relation — This article sets out the set theoretic notion of relation. For a more elementary point of view, see Binary relation. For a combinatorial viewpoint, see Theory of relations. For other uses, see Relation (disambiguation). In set theory and logic,… …
59Outline of logic — The following outline is provided as an overview of and topical guide to logic: Logic – formal science of using reason, considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and… …
60Outline of discrete mathematics — The following outline is presented as an overview of and topical guide to discrete mathematics: Discrete mathematics – study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have… …
