Question: Give the set of points of discontinuity of $f(x)= \lfloor x \rfloor$.
Answer: When $x=0.9999, y=0$ but when $x=1, y=1$, so for a very small change in the value of $x$, the change in the value of $y$ is big and this happens at all the integers (positive as well as negative), therefore the set of all the integers is the answer. Am I correct?