Prove that for any two real numbers a and b $\big||a|-|b|\big|< |a-b|$
128786
How to use triangle inequality to establish Reverse triangle inequality
33998
Show that given seven real numbers, it is always possible take two of them, such that $\left\vert\frac{a-b}{1+ab}\right\vert<\frac{1}{\sqrt{3}}$
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
140817
Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
143072
Proving $|\sin x - \sin y| < |x - y|$
69656
Prove or disprove that $\int_a^b |f(x)|\ \mathrm{d}x\geq \big | \int_a^b f(x)\ \mathrm{d}x\big| $
28391
Prove the compactness of a set B
3820
Prove that $||x|-|y||\le |x-y|$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
135750
Prove that if a and b are integers, then there are unique integers q and r such that $a = bq + r$, $-|b|/2 < r \le |b|/2$
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
154822
Properties of the composition law $a @ b= ab + b + a$ on the real numbers
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.