Symbol for intervals

Question

Set of integers is denoted by the symbol $\mathbb Z$, $\mathbb Q[x]$ stands for univariate polynomials over rationals, etc.

Is there a symbol which indicates the set of all open (or closed) intervals over $\mathbb Z$? I know there is $[a,b]$ (which apparently means over $\mathbb R$) but does something like $\mathbb Z^2$ make sense (it doesn't say $a<b$)?

Answer 1

How about $$[a,b]\cap\mathbb{Z}$$ to emphasize integers as opposed to reals.

Answer 2

In the context of interval analysis, the notation $\mathbb{I}\mathbb{R}$ is often used for the set of all closed intervals of the real line.