Prove that $|x| + |y| \le |x-y| + |x+y| $
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
31937
How do I prove equality of x and y?
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
29342
Prove the inequality: $(y+z)*x^4+(x+z)*y^4+(x+y)*z^4\le((x+y+z)^5)/12$ for positive reals.
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
20626
Prove that $x^y < y^x$
90896
proof of inequality $e^x\le x+e^{x^2}$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
101499
Prove $e^{x+y}=e^{x}e^{y}$ by using Exponential Series
136782
Prove that $x * y = \frac{x+y}{1+xy}$ is a stable part of $G=(-1, 1)$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
149889
Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$