Transitivity
From Wikinfo
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:
- <math>a R b \wedge b R c \Rightarrow a R c</math>
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.
References
- Adapted from the Wikipedia article, "Transitivity" http://en.wikipedia.org/wiki/Transitivity, used under the GNU Free Documentation License
