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Transitive closure
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. ...
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Talk:Transitive closure
Talk:Transitive closure Minimal inverse Is there an algorithm, that, given a transitive relation T, will return the smallest relation R such that the transitive closure of R is T? Is there ...
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Transitive reduction
Transitive reduction In mathematics, the transitive reduction of a binary relation R on ... math> on X such that that the transitive closure of is the same as the transitive closure of R. If the transitive ...
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Transitive set
Transitive set In set theory, a set (or class) A is transitive, if whenever x ∈ A, and y ... x is a subset of A. The transitive closure of a set A is the smallest (with respect to inclusion) transitive set B which contains A. Transitive ...
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Closure (mathematics)
Closure (mathematics) In mathematics, the closure C(X) of an object X is ... closed if it is equal to its closure. Typical structural properties of all closure operations are: The closure is increasing or extensive: the closure ...
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Transitive relation
Transitive relation In mathematics, a binary relation R over a set X is transitive if it holds for all a, b ... c \; \Rightarrow a R c Counting transitive relations Unlike other relation properties, it is ... general formula that counts the number of transitive relations on a finite set. However, there ... relations which are simultaneously reflexive, symmetric, and transitive Examples For example, "is greater than" ...
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Talk:Transitive reduction
Talk:Transitive reduction What about countably infinite graphs? It seems to me that the transitive reduction of the graph of "<" on the ... with the notation that S is the transitive closure): If S is antisymmetric, then the reduction ... If S is locally finite then the transitive reduction exists. Possibly the locally bounded ...
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Category:Closure operators
Category:Closure operators Pages in category "Closure operators" There are 19 pages in this section of this category. * Closure operator A Alexandrov topology Approach space C Closure (topology) Complete lattice F Fixed-point theorem ... Idempotence Interior (topology) Interior algebra K Kuratowski closure axioms L L (complexity) M Matroid ...
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Implementation of mathematics in set theory
... definition of "well-founded" below). The downward closure of an element x of the field ... x and y. A relation R is transitive if |
Binary relation
... of x≥y and y≥x, then x=y. transitive: for all x, y and z in ... xRz. "Is an ancestor of" is a transitive relation, because if x is an ancestor ... A relation which is reflexive, symmetric and transitive is called an equivalence relation. A relation which is reflexive, antisymmetric and transitive is called a partial order. A partial ... well-order. A relation which is symmetric, transitive, and extendable is also reflexive. Operations ...
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