How to prove that $\|x+y\|_p<\|x\|_p+\|y\|_p$?
138959
On the equality case of the Hölder and Minkowski inequalities
76267
Prove that: $x_1\cdot x_2\cdots x_n>y_1\cdot y_2\cdots y_m$.
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
26833
Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
143072
Proving $|\sin x - \sin y| < |x - y|$
3109
Prove that $(p+q)^m \leq p^m+q^m$
136427
Given $∃y.∀x.p(x,y)$, use the Fitch system to prove $∀x.∃y.p(x,y)$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
14677
Proving the exponential inequality: $x^y+y^x\gt1$
118039
How prove $p!|(a+1)$ if $p!|a^p+1$
148451
Polynomial inequality proof
20863
how do I prove this inequallity?
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$