Prove: Use the triangle inequality to prove that for all $x, y, | |x| − |y| | ≤ |x − y|$
3820
Prove that $||x|-|y||\le |x-y|$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
29198
How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
81618
Prove $||a|-|b| | \leq |a-b|$
91662
Proof for triangle inequality for vectors
143801
Proving the AGM inequality with 3 variables
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
31937
How do I prove equality of x and y?
77134
Proving a three variables inequality
126032
Proving a certain inequality
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
148451
Polynomial inequality proof
53112
Proving using AM-GM inequality
143072
Proving $|\sin x - \sin y| < |x - y|$
27911
How can I prove that $xy\leq x^2+y^2$?
15365
Proving that the triangle inequality holds for a metric on $\mathbb{C}$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.