# What is the equivalent of the integers symbol Z for n bit only integers?

We refer to the set of all integers as $$\mathbb{Z}$$. Now suppose we have a set of integers that can be held within a computer variable of $$n$$ bits width. Clearly they can only be of $$2^{n}$$ range, signed or not. How would we symbolise that? Is there something that is done to the zed, or does it remain simply $$\mathbb{Z}$$?

• You could always represent it as integers in the appropriate range, $\{i \mid i \in [0, 2^n] \land i \in \mathbb{Z}\}$. Or even more concisely: $[0, 2^n] \cap \mathbb{Z}$. Apparently wikipedia also mentions a notation for integer ranges: $[0 .. 2^n]$. – ryan Apr 20 at 1:47
• I guess technically it would only go from 0 to $2^n-1$ but you get the idea. Also see here. – ryan Apr 20 at 1:56

Specifically, $$[a,b]$$ means "real numbers between $$a$$ and $$b$$, inclusive", while $$[a\mathinner{\ldotp \ldotp}b]$$ means "integers between $$a$$ and $$b$$, inclusive". Changing any of the square brackets to curved means that endpoint is not included: $$a \not\in (a,b]$$, for example.
In this case, you'd want the interval $$[0\mathinner{\ldotp \ldotp}2^n)$$. Or, if you think the delimiters look mismatched and weird, you can use $$[0\mathinner{\ldotp \ldotp}2^n-1]$$.