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An example of a non-transitive relation with a less meaningful transitive closure is "x is the day of the week after y". The transitive closure of this relation is "some day x comes after a day y on the calendar", which is trivially true for all days of the week x and y (and thus equivalent to the Cartesian square , which is " x and y are both ...
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c then a < c; and if x ...
The relation , introduced as a notation for reduction sequences, may be viewed as a rewriting system in its own right, whose relation is the reflexive-transitive closure of →. Since a sequence of reduction sequences is again a reduction sequence (or, equivalently, since forming the reflexive-transitive closure is idempotent ), ∗ ∗ → ...
An example of a formal grammar with parsed sentence. ... is defined as the reflexive transitive closure of ... Though there is a tremendous body of literature on ...
Equivalently, the Church–Rosser property means that the reflexive transitive symmetric closure is contained in the joinability relation. Alonzo Church and J. Barkley Rosser proved in 1936 that lambda calculus has this property; [ 6 ] hence the name of the property. [ 7 ]
An example of an undirected hypergraph, ... In some literature edges are referred to as hyperlinks or connectors. [4] ... transitive closure, and shortest path problems.
In matroid theory, the closure of X is the largest superset of X that has the same rank as X. The transitive closure of a set. [1] The algebraic closure of a field. [2] The integral closure of an integral domain in a field that contains it. The radical of an ideal in a commutative ring.
Triadic closure is a concept in social network theory, first suggested by German sociologist Georg Simmel in his 1908 book Soziologie [Sociology: Investigations on the Forms of Sociation]. [1] Triadic closure is the property among three nodes A, B, and C (representing people, for instance), that if the connections A-B and A-C exist, there is a ...