Difference between revisions of "Equivalence class"
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==Definition== | ==Definition== | ||
| − | Given an [[Equivalence relation]] {{M|\ | + | Given an [[Equivalence relation]] {{M|\sim}} the equivalence class of {{M|a}} is denoted as follows: |
| − | <math>[a]=\{b|a\ | + | <math>[a]=\{b|a\sim b\}</math> |
==Equivalence relations partition sets== | ==Equivalence relations partition sets== | ||
Revision as of 09:48, 12 May 2015
Definition
Given an Equivalence relation [ilmath]\sim[/ilmath] the equivalence class of [ilmath]a[/ilmath] is denoted as follows:
[math][a]=\{b|a\sim b\}[/math]
Equivalence relations partition sets
An equivalence relation is a partition
Equivalence classes are either the same or disjoint
This is the motivation for how cosets partition groups.
TODO: Add proofs and whatnot
