$[a+b]\geq[a]+[b]$ for all a,b belongs to Real number
5222
$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
96133
Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
25623
Does $\sqrt{a+b} \le \sqrt a + \sqrt b$ hold for all positive real numbers a and b?
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
81618
Prove $||a|-|b| | \leq |a-b|$
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
23264
Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$