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9
Theorem 0.6 Equivalence Classes Partition
The equivalence classes of an equivalence relation on a set
constitute a partition of
. Conversely, for any partition
of
, there is an equivalence relation on
whose equivalence classes are the elements of ![](/pool/data/tex/44c29edb103a2872f519ad0c9a0fdaaa.gif)
![](/pool/data/tex/5dbc98dcc983a70728bd082d1a47546e.gif)
![](/pool/data/tex/5dbc98dcc983a70728bd082d1a47546e.gif)
![](/pool/data/tex/44c29edb103a2872f519ad0c9a0fdaaa.gif)
![](/pool/data/tex/5dbc98dcc983a70728bd082d1a47546e.gif)
![](/pool/data/tex/5dbc98dcc983a70728bd082d1a47546e.gif)
![](/pool/data/tex/44c29edb103a2872f519ad0c9a0fdaaa.gif)
![](/pool/img/avatar_40_40.gif)
Flashcard info:
Author: Squiggleart
Main topic: Mathematics
Topic: Abstract Algebra
School / Univ.: West Chester University
Published: 25.05.2011