If $c$ is a positive number, $|a|c \Leftrightarrow ac$
62172
Why does $-b < a < b \iff |a| < b$?
25921
Show that $\left(1+\dfrac{1}{n}\right)^n$ is monotonically increasing
152693
If $C|a$ and $C|b$ then $C|(ax+by)$
138107
Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
108084
Is it always true? $\left|A-B\right| \le \left|A\right| + \left|B\right|$
50266
In the following figure prove that: $AK||BC$
13224
Continuous function positive at a point is positive in a neighborhood of that point
137148
If $A=\left( \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{array} \right)$, find the rank of $A+A^2+A^3$
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
6970
If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.
97667
If $a<b$, $c<d$ then $a+c<b+d$?
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
34767
Proving $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)<3$ for all positive integers $n$
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $