An equivalence relation on a set is a Subset of , i.e., a collection of ordered pairs of elements of , satisfying certain properties. Write ``'' to mean is an element of , and we say `` is related to ,'' then the properties are

- 1. Reflexive: for all ,
- 2. Symmetric: Implies for all
- 3. Transitive: and imply for all ,

**References**

Stewart, I. and Tall, D. *The Foundations of Mathematics.* Oxford, England: Oxford University Press, 1977.

© 1996-9

1999-05-25