In general, the sequence of labels may contain duplicate values. This complicates the picture.

For now, let's focus on the normal case, where the labels are unique.

Def: a Series is **functional** if its labels are unique.

A functional Series obviously gives a function from labels to values, which permits us to make this equivalent definition:

Def: a **functional Series** is a function over a finite, totally ordered domain.

For now, let's focus on the normal case, where the labels are unique.

Def: a Series is **functional** if its labels are unique.

A functional Series obviously gives a function from labels to values, which permits us to make this equivalent definition:

Def: a **functional Series** is a function over a finite, totally ordered domain.