Difference between revisions of "Equivalence class"

 
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Given an [[equvalence 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>.
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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 16:18, 21 September 2006

Given an equivalence relation $R$ on a set $S$, the equivalence class of an element $s \in S$ is $\{ t \in S | R(s, t)\}$.


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 $\{\ldots, -10, -4, 2, 8, 14, \ldots\}$.

Given an equivalence class $C \subset S$, an element $c \in C$ is said to be a representative of that equivalence class.

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