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Was (wer) ist transitive closure - definition
transitive closure
The transitive closure R* of a relation R is defined by
x R y => x R* y
x R y and y R* z => x R* z
I.e. elements are related by R* if they are related by R
directly or through some sequence of intermediate related
elements.
E.g. in graph theory, if R is the relation on nodes "has an
edge leading to" then the transitive closure of R is the
relation "has a path of zero or more edges to". See also
Reflexive transitive closure.
Transitive closure
In mathematics, the transitive closure of a binary relation on a set is the smallest relation on that contains and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets it is the unique minimal transitive superset of .
Reflexive transitive closure
MATHEMATICAL PROPERTY OF AN OPERATION
Closure (binary operation); Closed under; Set closure (mathematics); Abstract closure; Axiom of closure; Abstract closure operator; Additively closed; Closure property of multiplication; Reflexive transitive closure; Reflexive transitive symmetric closure; P closure (binary relation); P closure; Reflexive symmetric transitive closure; Equivalence closure; Closure property; Congruence closure; Closure of a relation
Two elements, x and y, are related by the reflexive transitive
closure, R+, of a relation, R, if they are related by the
transitive closure, R*, or they are the same element.
Wikipedia
Transitive closure
In mathematics, the transitive closure of a binary relation on a set is the smallest relation on that contains and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets it is the unique minimal transitive superset of .
