Mathematical Notation – What Does z Subscript Something Mean?

Question

Decide a positive integer $N \in\mathbb Z$. Generate a uniformly distributed random positive integer sequence:
$$v_1, v_2, \ldots,v_n\in\mathbb Z_N$$
My question is, what does $\mathbb Z_N$ really mean here?
Does it mean something like the set of integers up to $N$?

Answer 1

Most often, one sees $\mathbb Z_n$ used to denote the integers modulo $n$, represented by $\mathbb Z_n = \{0, 1, 2, \cdots, n-1\}$: the non-negative integers less than $n$. So this correlates with the set you discuss, in that we have a set of $n$ elements, but here, we start at $n = 0$ and increment until we reach $n - 1$, where we stop, (since $n \equiv 0\pmod n$).