Mathematicians really can't be blamed for thinking that most
computer science is actually simple
applied mathematics invented by people who didn't even bother to look up the proper mathematical
terminology.
In mathematics, a 'relationship set' is called a relation. A many-to-one relation is called a function. A one-to-one relation is called an injective function.
For the terms 'one-to-one', 'many-to-one', etc. we can at least say that they are household words. But the term 'mapping cardinalities' is very confusing even to your fellow computer scientists. I've never heard it before. It suggests we're mapping cardinalities onto each other, which we're not, and it suggests infinite cardinalities, but they are finite (and typically, very small).
Booh!
P.S. It turn out that Database System Concepts, like many other textbook in introductory courses on relational databases, goes at some length to keep the presentation informal of what is fundamentally a formal mathematical theory. The authors purposely avoid all reference to actual mathematical notation or terminology; the phrase "mapping cardinalities" is just a symptom of this general approach. While informal, the resulting description is still accurate, but it is very incomplete; as soon as you try to use it for anything but trivial cases, you run into undefined areas.