Consider an integer $n$ where $a\leqslant n\leqslant b,\ a,b\in \mathbf R,\ b\gt a$. Then, we can denote it as
$$ n \in \mathbf X, \text{ where } \mathbf X := \{\, k\ |\ k\in \mathbf Z \land a\leqslant n\leqslant b\, \}. $$ But what if one doesn't want to define an extra set?
We know that $[\,a,b\,]$ is defined as
$$ [\,a,b\,] = \{\, x\ |\ x\in \mathbf R \land a\leqslant x\leqslant b\, \},\ a,b\in\mathbf R,\ b\gt a. $$
Then, can we denote $n$ (defined above) as
$$ n\in \mathbf Z \cap [\, a,b\, ],\ a,b\in \mathbf R,\ b\gt a \ ? $$ Is this notation okay? I haven't seen it anywhere.
Edit: fixed the last two lines as fleablood and Vsotvep pointed out
This notation is completely standard. Note that $\mathbb Z \cap [a,b]$ is the set of all real numbers (that are integers) living between $a$ and $b$ (including it, if any of these are integers).