# How to formulate a vector of discrete data

I am trying to formulate the following english sentence:

Let $v$ be a vector of dimension $9$ containing discrete data $x$ such that $x$ can only take the following values $\{-1,0,1\}$

My formulation:

Let $v = \{ x_i : x_i = \{-1,0,1\}\}_{i=1}^9$ be a discrete data vector.

Is this formulation correct?

What you currently have written implies each $x_i$ is a 3-vector, and $v$ is the set of all vectors equal to the vector $\{-1,0,1\}$. One modification would be to replace $=$ with $\in$, $$v = \{ x_i : x_i \in \{-1,0,1\}\}_{i=1}^9$$ Set builder notation works really well for infinite sets, but not so well for finite sets. One (not so pretty) alternative would be $$v = \{x_1, x_2,...x_9\} \quad x_i \in \{ -1,0,1\}$$