Prove $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y\rfloor+\lfloor x+y\rfloor$
5765
Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$
16337
Find the solution of $\lfloor \sin^{-1}(x)\rfloor>\lfloor \cos^{-1}(x)\rfloor$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
21802
Prove $\sum_{d \leq x} \mu(d)\left\lfloor \frac xd \right\rfloor = 1 $
138092
What is $\lfloor i\rfloor$?
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
107258
Proving If $k \le \left\lfloor \frac{n}{2} \right\rfloor$ then $\binom{n}{k-1} < \binom{n}{k}$
78356
How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
158463
Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
126632
Proving Inequalities with Absolute values
106979
Prove the inequality and limitation
17285
Proof of greatest integer theorem: floor function is well-defined
19064
Proof about floor function: $\lfloor x\rfloor+\lfloor x + \frac{1}{n} \rfloor+\cdots + \lfloor x + \frac{(n-1)}{n} \rfloor = \lfloor nx \rfloor$