nontransitivityとは 意味・読み方・使い方

名詞

nontransitivity (uncountable)

1. (logic, mathematics) The property of a binary relation that is not transitive; that is, there exist x, y, and z such that Rxy and Ryz hold but Rxz does not hold.
   • 1998, Hans Hermes, Introduction to Mathematical Logic, Springer, page 142:

     The relation is called nontransitive if it is not transitive, i.e., if there exist x, y, z with xRy, yRz, and not xRz.

使用する際の注意点

Nontransitivity is not to be confused with intransitivity or antitransitivity. A relation is intransitive if it is not transitive (nontransitive is a synonym for intransitive in some uses, but careful logicians distinguish them). A relation is antitransitive if Rxy and Ryz always imply not Rxz, which is stronger than mere nontransitivity. e.g. The relation "is a friend of" is often nontransitive: A may be friends with B, B may be friends with C, but A may not be friends with C.

同意語

• intransitivity (in some uses)

反意語

• transitivity

等位語

• antitransitivity