Prove that $|A| \geq |B|$ implies $|B| \leq |A|$
40586
There exists an injection from $X$ to $Y$ if and only if there exists a surjection from $Y$ to $X$.
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
28822
$|x| - |y| \leq |x-y|?$
143130
Proving that the supremum of $(a,b)$ is $b$.
149287
Prove that $A,B>0$ and $A_{ij}0$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
155884
What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
21737
If $A|B$ and $B|A$ then prove $A=\pm B$