If there is a function $f(x) = x\bmod n$ and, whenever $0\leq x_1\lt x_2\lt n$, we have $f(x_1)\lt f(x_2)$, can we say that $f$ is increasing?
Also, when finally I prove that $f(x)$ is increasing, how do I say it is doing so "modular arithmetically". I want to be able to specify that the function is increasing by the definition of increasing functions that is used for modular arithmetic.
Disclosure: I'm not a mathematician: I'm a student programmer who loves math. I'm working on proving that a given algorithm satisfies the requirements for being a solution to the critical section problem. This is homework, but the answer to that question is not homework.
PS I post on stackoverflow but this is my first question here.