Representing the set which contains integers each of which is a subset of certain interval(segment?).

Question

I've read the book of cyber security and saw the notation below.

$$ \mathbb{Z_{n}} ~~\leftrightarrow~~ \text{set of integers which satisfy }~ 0 \leq i < n $$

And what I want to represent is the set of natural integers equal or greater than 1 and less than n+1

$$ ~~~\uparrow \left( 1 \leq i \leq n \right) ~$$

Is there some good notation(s)?

Can I write it as $~ \mathbb{N_{n+1}} ~$ ? which notation is correct?

I know using $~ \mathbb{Z_{n+1}} \setminus \left\{ 0 \right\} ~$ is one of the ways but seemingly bit complicated for me.

The usual notation for the set ${1,2,\dots,n}$ is $[n]$. – bof Jul 18 '21 at 01:57 — bof, Jul 18 '21 at 01:57

score 1 · Accepted Answer · answered Jul 18 '21 at 01:49

From proofwiki page, a possible notation is $$\mathbb{N}_n^*=\{x \in \mathbb{N}^*: x \le n\}= \{ 1,2, \ldots, n\}$$

$\mathbb{N}_{n+1}$ includes the element $0$ according to the page as well.

Do remember to define it explicitly in your work to avoid confusion of your readers.

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