Often I need to write something like $n \in \{1,...,N\}$ or $n \in \{-N,...,N\}$ in subscripts and sums. I'd like to use something a bit shorter. Looking around at all the notation questions on Math.SE I came up with the following:
$$ n \in \{1,...,N\} \rightarrow n \in \mathbb{Z}^+_{\le N}$$
$$ n \in \{-N,...,N\} \rightarrow |n| \in \mathbb{Z}_{\le N}$$
Is there any better notation I could use that is also short? Or should I just define my own notation like $\{1,...,N\} = \mathbb{Z}^N, \{-N,...,N\} = \mathbb{Z}^{|N|}$
I've seen $[n]$ to mean $\{1,\dots,n\}$. This is used, for example, in the wonderful book generatingfunctionology. Don't assume your readers will be familiar with it, though; you should explain your notation in the text or a footnote.