relation closure

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• Closure (mathematics) — For other uses, see Closure (disambiguation). In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers… …   Wikipedia

• Closure 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… …   Wikipedia

• Binary relation — Relation (mathematics) redirects here. For a more general notion of relation, see Finitary relation. For a more combinatorial viewpoint, see Theory of relations. In mathematics, a binary relation on a set A is a collection of ordered pairs of… …   Wikipedia

• Transitive closure — In mathematics, the transitive closure of a binary relation R on a set X is the smallest transitive relation on X that contains R .For example, if X is a set of airports and xRy means there is a direct flight from airport x to airport y , then… …   Wikipedia

• Reflexive relation — In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation on S where x x holds true for every x in S.[1] For example, could be is equal to . Contents 1 Related terms 2… …   Wikipedia

• Transitive relation — In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b , and b is in turn related to an element c , then a is also related to c . Transitivity is a key property of both partial order… …   Wikipedia

• Equivalence relation — In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being equivalent in some way. Let a , b , and c be arbitrary elements of some set X . Then a b or a ≡ b denotes that a is… …   Wikipedia

• Well-founded relation — In mathematics, a binary relation, R, is well founded (or wellfounded) on a class X if and only if every non empty subset of X has a minimal element with respect to R; that is, for every non empty subset S of X, there is an element m of S such… …   Wikipedia

• Cognitive closure (philosophy) — Problems of inquiry Cognitive closure (philosophy) Cognitive bias (psychology) Empirical limits in science This box: view · talk · …   Wikipedia

• ancestral relation — Intuitively, a relation that stands to another as ‘ancestor of’ stands to ‘parent of’: an ancestor is a parent, or parent of a parent, and so on. The formal definition of the ancestral is due to Frege . Suppose, to simplify, we allow that y is… …   Philosophy dictionary

• Migraines associated with PFO heart defect — PFO, or patent foramen ovale, is a heart valve in humans that usually closes off at or shortly after birth. The valve’s function is to let the circulating blood bypass the lungs, which the body doesn t rely on until a newborn starts breathing air …   Wikipedia