Transitive_relation Transitive_relation

Transitive relation - Definition and Overview

Related Words: Adverbial, Brittle, Copula, Correct, Deciduous, Dying, Ephemeral, Fading, Flying, Formal, Fragile

In mathematics, a binary relation R over a set X is transitive if it holds for all a, b, and c in X, that if a is related to b and b is related to c, then a is related to c.

In mathematical notation, this is:

<math>\forall a, b, c \in X,\ a R b \and b R c \; \Rightarrow a R c<math>

For example, "is greater than" and "is equal to" are transitive relations: if a = b and b = c, then a = c.

On the other hand, "is the mother of" is not a transitive relation, because if Alice is the mother of Brenda, and Brenda is the mother of Claire, then Alice is not the mother of Claire.

Examples of transitive relations include:

A transitive relation that is also reflexive is a preorder. A preorder that is antisymmetric is a partial order. A preorder that is symmetric, is an equivalence relation.

See also transitive closure, Intransitivity

Example Usage of Transitive

kimarx: @hanekomu But Japanese language doesn't definitely distinguish inTransitive from Transitive, so, 'Shibuya he aruku' isn't wrong.
mjohn206: LOVE is the MOVEMENT. JESUS is LOVE. Thus, by the Transitive property.. JESUS is the MOVEMENT. endofstory.
delajed: Photoshop is fun. School is teaching me how to use Photoshop. Transitive relation? Yes.
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