Editing Transitive relation (section)

{{Short description|Type of binary relation}}
{{Infobox mathematical statement
| name = Transitive relation
| type = [[Binary relation]]
| field = [[Elementary algebra]]
| statement = A relation <math>R</math> on a set <math>X</math> is transitive if, for all elements <math>a</math>, <math>b</math>, <math>c</math> in <math>X</math>, whenever <math>R</math> relates <math>a</math>  to <math>b</math> and <math>b</math> to <math>c</math>, then <math>R</math> also relates <math>a</math> to <math>c</math>.
| symbolic statement = <math>\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc</math>
}}

In [[mathematics]], a [[binary relation]] {{mvar|R}} on a [[set (mathematics)|set]] {{mvar|X}} is '''transitive''' if, for all elements {{mvar|a}}, {{mvar|b}}, {{mvar|c}} in {{mvar|X}}, whenever {{mvar|R}} relates {{mvar|a}}  to {{mvar|b}} and {{mvar|b}} to {{mvar|c}}, then {{mvar|R}} also relates {{mvar|a}} to {{mvar|c}}.

Every [[partial order]] and every [[equivalence relation]] is transitive. For example, less than and [[equality (mathematics)|equality]] among [[real number]]s are both transitive: If {{math|''a'' < ''b''}} and {{math|''b'' < ''c''}} then {{math|''a'' < ''c''}}; and if {{math|''x'' {{=}} ''y''}} and {{math|''y'' {{=}} ''z''}} then {{math|''x'' {{=}} ''z''}}.