S is a finite set show that $|P(S)|$ is $2^{|S|}$.
44214
The number of subsets of a set of cardinality $n$
12857
Induction proof: $S$ contains powers of 2 and predecessors implies $S={\bf N}$
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
28223
Prove/Disprove that if two sets have the same power set then they are the same set
151544
Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
145873
Let $X$ and $Y$ be finite sets. Then the set $Y^X$ is finite and $\#(Y^X) = (\#Y)^{\#X}$.
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
128305
$PGL(n, F)=PSL(n, F)$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
25834
Proof a set cannot contain its own powerset - Russell's Paradox
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
33894
How many chains are there in a finite power set?
121141
Proving Finiteness of Group from Presentation
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
71133
prove inequlity about cardinality power sets