Difference between revisions of "Equivalence relation"
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Revision as of 22:17, 23 June 2006
Let be a set. A relation on is said to be an equivalence relation if satisfies the following three properties:
1. For every element , . (Reflexive property) 2. If such that , then we also have . (Symmetric property) 3. If such that and , then we also have . (Transitive property)
Some common examples of equivalence relations:
- The relation (equality), on the set of real numbers.
- The relation (congruence), on the set of geometric figures in the plane.
- The relation (similarity), on the set of geometric figures in the plane.
- For a given positive integer , the relation (mod ), on the set of integers.