Notation for a particular number

The maximum value of $X$ is $Y$.

$Y \ge 0$

$Y$ is in increments of $1$.

How can I use a concise notation set to show the range of valid $X$ values?


Solution 1:

$X=\{x\in \mathbb{Z} \cap [0,y]: y\in \mathbb{N} \cup \{ 0 \} \}$

Solution 2:

How about this: $X \in \{0,1,2,\ldots,Y\}$. More succinctly, $X \in [0, Y]$.