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transitive relation
Sign in to savebinary relation R with the property that xRy and yRz implies xRz
Key facts
- Type
- Binary relation
- Field
- Elementary algebra
- Symbolic statement
- ∀ a , b , c ∈ X : ( a R b ∧ b R c ) ⇒ a R c {\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc}
via Wikipedia infobox
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Encyclopedic overview
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.
Excerpted from Wikipedia’s “transitive relation” article, available under the CC BY-SA 4.0 licence.