I know, logically it makes sense that the floor and ceiling both equal x, when x is an integer. Any proofs I've read really only use reasoning to explain this. I'm wondering if there is a way to use inequalities to prove this instead?
I know that it is stated here: https://en.m.wikipedia.org/wiki/Floor_and_ceiling_functions
Under relations among functions, but I'm unsure of how they arrived there.