EquivalenceClass.md (691B)
1 # Equivalence Class 2 3 AM W14 Video 4 5 **Definition:** An equivalence class is a subset of a set relation that describes a given output and all elements of the sort denoted by [X]. 6 7 A simple example of this is the mod 5 relation. There are only five values that can result from mod 5 for the set $\Z$ being 0,1,2,3, and 4. Each of these can be defined as its own equivalence class denoted by [0], [1], [2], [3], and [4]. For a class to be an equivalence class, the relation must be an equivalence relation. Additionally we know [0] = [5] = [10] and no two sets are equivalent to each other. The final interesting thing is that the intersection between any of these sets is always the null set.