Ad
related to: transitive closure of relationship rules in geometry pdf free
Search results
Results from the WOW.Com Content Network
In mathematics, the transitive closure R + of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets R + is the unique minimal transitive superset of R .
However, the transitive closure of a restriction is a subset of the restriction of the transitive closure, i.e., in general not equal. For example, restricting the relation "x is parent of y" to females yields the relation "x is mother of the woman y"; its transitive closure does not relate a woman with her paternal grandmother. On the other ...
The transitive extension of R 1 would be denoted by R 2, and continuing in this way, in general, the transitive extension of R i would be R i + 1. The transitive closure of R, denoted by R* or R ∞ is the set union of R, R 1, R 2, ... . [8] The transitive closure of a relation is a transitive relation. [8]
A relation is transitive if it is closed under this operation, and the transitive closure of a relation is its closure under this operation. A preorder is a relation that is reflective and transitive. It follows that the reflexive transitive closure of a relation is the smallest preorder containing it
In mathematics and theoretical computer science, a Kleene algebra (/ ˈ k l eɪ n i / KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes the theory of regular expressions: it consists of a set supporting union (addition), concatenation (multiplication), and Kleene star operations subject to certain algebraic laws.
In set theory, a set x is called a well-founded set if the set membership relation is well-founded on the transitive closure of x. The axiom of regularity, which is one of the axioms of Zermelo–Fraenkel set theory, asserts that all sets are well-founded.
The closure on K n is the closure in the Zariski topology, and if the field K is algebraically closed, then the closure on the polynomial ring is the radical of ideal generated by S. More generally, given a commutative ring R (not necessarily a polynomial ring), there is an antitone Galois connection between radical ideals in the ring and ...
A transitive set (or class) that is a model of a formal system of set theory is called a transitive model of the system (provided that the element relation of the model is the restriction of the true element relation to the universe of the model). Transitivity is an important factor in determining the absoluteness of formulas.
Ad
related to: transitive closure of relationship rules in geometry pdf free