Prove that $⌊xy⌋ \le ⌊x⌋⌊y⌋ + ⌊x⌋+⌊y⌋$ for $x,y \in \mathbb{R}$, as $x,y>0$
13953
Floor function of a product
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
27911
How can I prove that $xy\leq x^2+y^2$?
108704
Help with proof of $|x+y| \geq |x|-|y|$
122944
Prove $|y''(x)| \leq 40$ for all $x \in [1,3]$.
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$