Is it possible to prove that ceil(x/y) = ceil(ceil(x)/ceil(y))?

Question

Let $\operatorname{ceil}(x)$ be the smallest integer greater than or equal to $x$. (Also denoted $\lceil x\rceil$.)

Is it true that $\operatorname{ceil}(x/y) = \operatorname{ceil}(\operatorname{ceil}(x)/\operatorname{ceil}(y))$?

It would help me out if this would be provable but I am not that familiar with the ceil and floor functions in mathematics. I am not sure what properties I could apply.

Answer 1

The statement is not true.

Consider $x=0.9$ and $y=0.1$ then $\lceil\frac{x}{y}\rceil=9$ while $\lceil\frac{\lceil x\rceil}{\lceil y\rceil}\rceil=1$