Show that no set $S$ is equinumerous with $P(S)$.
4467
Proving Cantor's theorem
25834
Proof a set cannot contain its own powerset - Russell's Paradox
37783
Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
54496
Showing that $\mathbb{R}$ and $\mathbb{R}\backslash\mathbb{Q}$ are equinumerous using Cantor-Bernstein
83542
A natural problem in $\textrm{S}_2^\textrm{P}$?
146055
Proving a set of functions is uncountable
37331
Prove that every set with more than one element has a permutation without fixed points
93771
Prove that for any set $A$ there is some $x \notin A$
132382
Showing a set is nowhere dense in $C([0,1])$
47639
Uncountable Cartesian product of closed interval
119886
The cantor set is uncountable
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
67066
Proof there is a 1-1 correspondence between an uncountable set and itself minus a countable part of it
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
113083
How to prove a set equality?
146098
Number of nonempty subsets of a set with $n$ elements