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Transitive relation
| Type | Binary relation |
|---|---|
| Field | Elementary algebra |
| Statement | A relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . |
| Symbolic statement |
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 = y and y = z then x = z.
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