An equation in floor function with two variables

Question

Let us consider the following equation with respect to $x$ and $y$:

$$⌊x⌋=⌊y⌋$$

My question is how to obtain the unknowns $x$ and $y$. I have no idea to start.

Answer 1

You can't. We could have $x = 2, y = 2.9$. Or we could have $x = 10034.7$ and $y = 10031 + \pi$. Or any number of other possibilities.

All we can tell from $\lfloor x\rfloor = \lfloor y \rfloor$ is that there is some integer $n$ such that $x, y\in [n, n+1)$.