How to prove that $\lfloor a\rfloor+\lfloor b\rfloor\leq \lfloor a+b\rfloor$
5222
$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$
105641
Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
106979
Prove the inequality and limitation
127983
Does $\lim_{x \to 0+} \left(x\lfloor \frac{a}{x} \rfloor\right)=a?$
82803
Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
79836
Proof for $\left\lfloor\frac 1j\left\lfloor\frac nk\right\rfloor\right\rfloor=\left\lfloor\frac n{jk}\right\rfloor$
117262
Proving a logarithm inequality
40973
How to find $\lfloor 1/\sqrt{1}+1/\sqrt{2}+\dots+1/\sqrt{100}\rfloor $ without a calculator?
108704
Help with proof of $|x+y| \geq |x|-|y|$
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
146023
How to prove that $x^2 - \lfloor x\rfloor^2$ is onto?
158463
Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$
5934
How to prove floor identities?
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
156831
Prove $\Sigma_{k=0}^{n-1}\lfloor x+\frac{k}{n}\rfloor=\lfloor nx\rfloor$ , n is a Natural Number