In this usage of "map", the intended meaning is to determine the relation between
cardinalities. To quote the dictionary sitting next to me, cardinality is "the number of elements in a given
mathematical set." Combine the two and we have "determine the relation between the number of elements in either set." This is exactly what we are striving for. Since this is a phrase often used when talking about
relational databases, it is safe to asssume that the intent is to define legal ways for
tables to relate to one another.
One common mistake made by
mathematicians and even other
computer scientists is in mistaking the terminology of one
discipline for another. For example, most biologists don't barge into a lecture on
data structures and insist that the term
tree isn't accurate, since it's upside down. And even if it was turned right side up, the root would extend further and branch out, not to mention a plethora of other simplifications. There are two reasons they don't do this. One,
biologists and
computer scientists are usually not crammed into the same room for extended periods of time. Two, they realize that any given group of
academics will develop their own '
dialect' that is only meaningful to other academics in the same
discipline.
In closing, I would like to apologize to
Georg Cantor and
rp for ever having used "
cardinality" to describe the size of a finite set.