I have the following problem:
Find all of the points of discontinuity and the points of removable discontinuity of the following function:
$f(x,y)=\left\lfloor\frac{x}{y}\right\rfloor$, where $\lfloor t\rfloor$ is the whole part of the number $t$.
It makes sense that at $y=0$ we would have a point of discontinuity and that it would not be removable, but it can't be that simple, right? I can't understand what part the whole part of the number plays either in this problem.
I would appreciate it if someone could help.
Your function is not even defined when $y=0$ and therefore it makes no sense to say that it is discontinuous there.
On the the other hand, note that $\lim_{x\to0^-}\lfloor x\rfloor=-1\neq\lfloor0\rfloor$. Can you take it from here?