The well-known notation for continuous intervals is $[a,b]$. But what's the case for discrete intervals? Actually they are sets of finite elements $\left\{a, a+1, ..., b-1, b\right\}$ or infinite elements $\left\{0, 1, 2, ...\right\}$.
Is there any special notation or common practice for discrete intervals?
A notation that is sometimes used is double-brackets, so $[[a,b]]$. (But it should still be explained what is meant.)
If one uses only the discrete version it is not uncommon to just use the usual notation $[a,b]$ for the discrete version, and to say so clearly somewhere.
Let me add that on an earlier question regarding this subject the notations $a..b$ and $[a..b]$ were also mentioned.
In the book Statistics for Business and Economics by David R. Anderson,
Discrete intervals are simplified using ellipses. For instance:
B = 0, 1, 2, …, 20
E = 0, 1, 2, …, 50
V = 0, 1, 2, …, ∞
Unlike continuous intervals, which can be described using parentheses and square bracket, or inequality symbols, Like:
H = [0,8] or 0 ≤ H ≤ 8
K = (0, ∞) or K > 0
