Cardinals proof |A| ≤ |B| iff |B| ≥ |A|
40586
There exists an injection from $X$ to $Y$ if and only if there exists a surjection from $Y$ to $X$.
149287
Prove that $A,B>0$ and $A_{ij}0$
48278
Inequality about infinite cardinals
84198
Step in Proof of Cardinality of Product of two Groups
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
62936
Proving equivalencies of two versions of the Axiom of Choice
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
5840
divides, not divides and cardinalities
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
23141
How to prove that from "Every infinite cardinal satisfies $a^2=a$" we can prove that $b+c=bc$ for any two infinite cardinals $b,c$?
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
77286
Proving set theory question