If and , then if and only if
If is nonempty, then is nonempty
For , the equivalence class containing is often denoted by , so that
The set of all equivalence classes of under is defined to be the set of all subsets of which are equivalence classes of under , and is denoted by . The map is sometimes referred to as the .
For any equivalence relation , the set of all equivalence classes of under is a partition of , and this correspondence is a bijection between the set of equivalence relations on and the set of partitions of (consisting of nonempty sets).
|Date of creation||2013-03-22 11:52:30|
|Last modified on||2013-03-22 11:52:30|
|Last modified by||mathcam (2727)|