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?
On
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
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.