Transitivity

Mathematical definition

Transitivity is in logic and mathematics. If the following statements remain valid for all a, b, and c ∈ X, then the binary relationship R on the set is transitive: "If a is related to b and b is related to c, then a is related to c."

Chinese name: Transitivity
Foreign name: transitivity

Discipline: mathematics
application area: Algebra

catalog

one Mathematical representation
two example

Mathematical representation

Announce

edit

, where

For some Relational Operators 。

Then:

example

Announce

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Relational Operators

Meet the delivery relationship: if

。

There are other examples:

Equal relation

Inclusion of sets

Same sign unequal relationship

Divisive relation

The transitive relationship satisfying reflexivity is called Preorder relation 。 The preorder relation satisfying antisymmetry is called Partial order relation 。 The pre order relation satisfying symmetry is called equivalence relation 。

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