# 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 '19 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 '19 at 1:56

For bounded sets, the usual convention is to use interval notation.

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 $$[0\mathinner{\ldotp \ldotp}2^n-1]$$.

P.S. LaTeX doesn't have a builtin for "two dots", so I used \mathinner{\ldotp \ldotp} from this answer.

• In here it looks like \enleadertwodots could work, but not quite. There's also \hdotdot which is weird why they don't have \ldotdot.
– ryan
Apr 20 '19 at 2:29
• @ryan Ah, good find! And yeah, I'm surprised \ldotdot isn't a standard symbol, since I've seen this in more papers than many of the other mathfont symbols. But, it's not too hard to fake, thankfully. Apr 20 '19 at 2:32
• Actually yes, \enleadertwodots works perfect (well, maybe not perfect, but close) if you use the stix package. However, the name is not very appealing.
– ryan
Apr 20 '19 at 2:40
• Here, you can see for yourself: tex.stackexchange.com/a/485694/138833.
– ryan
Apr 20 '19 at 2:48