Let $a,b\in \{\operatorname{Re}(z) <0\}$ then $|e^a - e^b | < |a-b|$.
16852
$|e^a-e^b| \leq |a-b|$ for complex numbers with non-positive real parts
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
136835
ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
153355
Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
156541
$a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
100968
Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.