For all real numbers between 0 and 1 (closed interval), we can write $[0,1]$ or $\{x\in \mathbb{R} : 0\leq x \leq 1\}$.
For all integers between 0 and 1 (closed interval), we can write $[0 .. 1]$ or $\{x\in \mathbb{Z} : 0\leq x \leq 1\}$. Alternatively, we can write $\{0,1\}$.
However, I find writing the interval as [0,1] can sometimes be a little ambiguous as some refer it to an integer interval. Hence would the following notations serve as valid and natural alternatives?
$\mathbb{R}[0,1]$ or $[0,1]_\mathbb{R}$
$\mathbb{Z}[0,1]$ or $[0,1]_\mathbb{Z}$