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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 ...
Poetic closure is the sense of conclusion given at the end of a poem. Barbara Herrnstein Smith's detailed study—Poetic Closure: A Study of How Poems End—explores various techniques for achieving closure. One of the most common techniques is setting up a regular pattern and then breaking it to mark the end of a poem.
The semantics for the common knowledge operator, then, is given by taking, for each group of agents G, the reflexive (modal axiom T) and transitive closure (modal axiom 4) of the , for all agents i in G, call such a relation , and stipulating that is true at state s iff is true at all states t such that (,).
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 ...
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.
The opposite is a prologue—a piece of writing at the beginning of a work of literature or drama, usually used to open the story and capture interest. [2] Some genres, for example television programs and video games, call the epilogue an "outro" patterned on the use of "intro" for "introduction".
An example in modern English is the verb to arrive. Verbs that can be used in an intransitive or transitive way are called ambitransitive verbs. In English, an example is the verb to eat; the sentences You eat (with an intransitive form) and You eat apples (a transitive form that has apples as the object) are both grammatical.