Show that $||x|-|y||≤|x-y|$
91662
Proof for triangle inequality for vectors
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
20467
Show that $(y_n)\in l^q$
116382
Showing convexity of a function with the restriction over an arbitrary line
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
5765
Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
132971
Prove that $|a| < b \iff -b<a<b$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
152311
Proving expression$\geq 2$, where variables are $x,y,z$
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
3820
Prove that $||x|-|y||\le |x-y|$
8207
Can I prove this inequality algebraically?
31937
How do I prove equality of x and y?
108704
Help with proof of $|x+y| \geq |x|-|y|$