So this is definitely down to how you define the word, but by the above definition, shouldn't Globally Unique Identifiers be called Globally Distinctive Identifiers?

Also, because my brain has been damaged by modern programming languages, it seems like uniqueness should be defined as (please excuse my rusty logic syntax):

R = resumes, r \in R, unique(r) -> (\forall s \in R-{r}, r != s) (for some definition of equality).

A finite collection of distinct values constitutes a set.

A collection of unique values constitutes a set with exactly one element.