For all $x$ which are real numbers, prove that $\lfloor 2x\rfloor = \lfloor x\rfloor + \lfloor x+0.5\rfloor.$
5914
Proving $\lfloor 2x \rfloor = \lfloor x \rfloor + \lfloor x+0.5\rfloor$
22087
Find all real numbers x such that $ |5x-1| ≤ |3x-2|$
8617
How do you prove ${n \choose k}$ is maximum when $k$ is $ \lceil \tfrac n2 \rceil$ or $ \lfloor \tfrac n2\rfloor $?
101899
Proof By Induction of a Sum
40779
What is the smallest possible value of $\lfloor (a+b+c)/d\rfloor+\lfloor (a+b+d)/c\rfloor+\lfloor (a+d+c)/b\rfloor+\lfloor (d+b+c)/a\rfloor$?
47923
For $n\in\mathbb{N}$, evaluate $\int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$
45480
Does $\sum\frac{(-1)^{\lfloor \sqrt n\rfloor}}{ n}$ converge?
106011
Proving it has all real roots
143306
Limit involving floor function: $\lim\limits_{x\to 0} x \left\lfloor\frac1x \right\rfloor$
138092
What is $\lfloor i\rfloor$?
137016
Showing that $\lfloor\frac{x-1}3\rfloor=\lfloor\frac{x}3+\frac23\rfloor-1$ and $\lfloor\frac{x+1}3\rfloor=\lfloor\frac{x}3+\frac13\rfloor$.
1449
Floor function properties: $[2x] = [x] + [ x + \frac12 ]$ and $[nx] = \sum_{k = 0}^{n - 1} [ x + \frac{k}{n} ] $
158463
Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$
115101
Solve $x + \lfloor y \rfloor + \{ z \} = 13.2$; $\{ x \} + y + \lfloor z \rfloor = 15.1$; $\lfloor x \rfloor + \{ y \} + z = 14.3$
17285
Proof of greatest integer theorem: floor function is well-defined
63505
Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $
99483
If $T(n+1)=T(n)+\lfloor \sqrt{n+1}, \rfloor$ $\forall n\geq 1$, what is $T(m^2)$?