Proof By Counterexample, pigeonhole This is from a discrete math homework question. I really don't know where to begin, except that I understand the concept of a proof by counterexample, just not how to get to it.
In the statement of the pigeonhole, we argued that $$\left\lfloor\frac{n-1}m\right\rfloor+1=\left\lceil\frac{n}m\right\rceil\;.$$
Prove that this is generally not true.

HINT: The identity
$$\left\lfloor\frac{n-1}m\right\rfloor+1=\left\lceil\frac{n}m\right\rceil$$
is valid for positive integers $m$ and $n$, so you’ll have to look elsewhere for a counterexample. What if $m=-1$ and $n$ is some positive integer? what if $m=1$ and $n$ is not an integer at all?
