How to formally write a sign sequence?

Question

Is it correct way to write sign sequence:

$\{a_i\}_{i=1}^N|a_i \in \{+1, -1\}$

?

I try writing the following: "Finite sequence of N elements when each element is +1 or -1". Am I right?

Answer 1

Yours seems to be fine. Alternative is to regard the sequence as a function $$a:\mathbb{N} \to \{-1,1\}.$$ That is, $a_n$ is a function that takes as an argument a natural number $n$ and indicates if this term is $-1$ or $1$.