Show that the equivalence classes give a partition of $X$.
93952
Show that $X$ can be represented as a union of disjoint equivalence classes
104349
Proof by induction involving symmetric groups
70409
Rational Equivalence Relation and Measure
36566
Equivalence classes and metric spaces
83615
split conjugacy class in $S_n$ into two equal size conjugacy classes in $A_n$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
20615
How many Nerode equivalence classes does the language $x\neq y$ have?
110018
Conjugacy classes in $A_n$.
69043
The equivalence relation generated by a relation
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
62455
Prove Equivalence Relation in G
128716
Intuitive/direct proof that a rectangle partitioned into rectangles each with at least one integer side must itself have an integer side
41693
Use irreducible fibers to show $X$ is irreducible
76347
Shorter proof for some equvalences
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
51914
Show that $S$ is compact.
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers