Does $|A|^{|A|}=2^{|A|}$ hold for any infinite set $A$?
118212
Is it true that $A^A\simeq P(A)$?
130998
Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
8494
Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
27675
Polynomials vanishing on an infinite set
127242
$|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
86154
Why is this true? A set is Dedekind infinite if and only if equipotent to the union with the set containing itself
44706
Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$
9082
Do sets, whose power sets have the same cardinality, have the same cardinality?
98470
If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
3072
If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
5022
Can a set containing $0$ be purely imaginary?
62208
If $A$ is a non-empty set, then $A \notin A$
36281
A set is infinite iff it is equivalent to a proper subset of itself
22391
Is the set of all pairs of real numbers uncountable?
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?