Difference between revisions of "Equivalence class"
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| − | Given an [[ | + | Given an [[equivalence relation]] <math>R</math> on a set <math>S</math>, the '''equivalence class''' of an element <math>s \in S</math> is <math>\{ t \in S | R(s, t)\}</math>. |
Latest revision as of 17:18, 21 September 2006
Given an equivalence relation 
on a set 
, the equivalence class of an element 
is 
.
For example, the relation "equivalence modulo 6" is an equivalence relation on the integers. The equivalence class of 2 under this relation is the set of all those integers which are equivalent to 2, in other words 
.
Given an equivalence class 
, an element 
is said to be a representative of that equivalence class.
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