Correct representation of a range in mathematics

Question

Denote $X_{max}$ and $X_{min}$ as minimum and maximum seperation distance and X obeys a uniform distribution satisfying $(0 \leq X_{min} < X_{max})$. Is it correct to represent it as $[X_{min}, X_{max}]$? I am aware there are some mathematical representations like $[X_{min}, X_{max})$ and $(X_{min}, X_{max}]$ but I am not sure if it fits into this context. I would appreciate a detailed answer that others might benefit from.

Answer 1

If the real values of $x$ are such that $a \leqslant b\leqslant x$, we can write this in interval notation $a\in [a,b]$. If $a<x< b$, we write $x\in (a,b)$. For $a \leqslant x<b$ we write $x\in [a,b)$ and $x\in (a,b] $ for $a< x\leqslant b$.

The strict inequality in your firs line implies that you have a distribution (otherwise interval length allowed could be zero).