Transitivity
In mathematics, transitivity is a mathematical property of binary relations such that if A and B are related, and B and C are related, then it follows that A and C are also related, for all A, B, and C for which the relation may apply. The relation is then said to be transitive.
In notation, this is:
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.
Example of transitive relations include:
If a transitive relation is also reflexive and symmetric, then it is said to be an equivalence relation.
See also Transitive closure.
Referenced By
Linear order | Linearly ordered set | List of basic discrete mathematics topics | List of mathematical topics (S-U) | Order topology | TotalOrderedSet | Total order | Total ordered set | Totally ordered | Totally ordered set
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