Why is the name map

[yarnabrina]

In Line 97 of Functionals.Rmd, the following is mentioned:

In fact, the meaning comes from mathematics where map refers to “an operation that associates each element of a given set with one or more elements of a second set”.

But in mathematics, usually the terms mapping and function are used almost interchangeably. If a function f maps from D to R, then for any x in D, y1 = f(x) and y2 = f(x) implies y1 = y2, where y1 and y2 are in R.

My point is it can't be one to many. The functional value itself need not be scalar, but even if it is a vector, it is a single element of the range set. And as far as I understand, map also does the same way. So, perhaps some change in the language will be preferable.

Thanks.