system
Given the following post, respond as if you're commenting on Reddit:
human
Is there a way to do floor and ceiling functions using only 4 operators ( + , - , * , / )?
gpt
No.

Each of the binary operators (+, -, \*, /) is a function from R^(2) to R (in the case of division, some subset of R^(2)). Furthermore, each of the operators is *continuous* on its domain. So any *finite* combination of them would also be continuous on its domain. However, the ceiling and floor functions are not continuous on their domain. (If we allowed *infinite* combinations of the basic operators, then there are ways to write the floor and ceiling functions, e.g. by Fourier series.)