Does $|X|<|Y|$ imply $\mathcal{P}(X)<\mathcal{P}(Y)?$
21663
Bijection between power sets of sets implies bijection between sets?
85818
$E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
47810
$C(X)$ is separable when $X$ is compact?
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
15354
Formal proof of $\exists x \forall y P(x,y) \implies \forall y \exists x P(x,y)$
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
153355
Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
71725
$\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ notation
67717
$A \oplus B = A \oplus C$ imply $B = C$?
3820
Prove that $||x|-|y||\le |x-y|$
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
66610
Finding a correspondence between $\{0,1\}^A$ and $\mathcal P(A)$
5293
Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
25187
Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
89034
For any $\epsilon$, if $\epsilon>0$ and $|x|<\epsilon$, then $x=0$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$