What is a formal definition of the unique values in an array? Let the term unique be defined as all other values of this object are numerically different from one value of this object.
Let $v$ be a vector with 5000 observations with each observation may or may not be unique.
What is a formal way to state that one only considers the unique values of $v$?

Adopting the notion of set, I believe it is possible to define as follows:
Let $v$ be any element of $V$, the set of unique elements of V is given by
$$\bigcup_{\forall v \in V} v$$
