George Cantor is credited as the founder of modern set theory, but other important mathematicians like Dedekind, Zermelo, Fraenkel, Russel, and Godel have made major contributions.

For economics the answer is Alfred Marshall.

P F J M Eligh has written "Shakes and Modules" a book that explains and provides examples of how to use (e.g., module) Zermelo-Fraenkel set theory to reason about (e.g., shake) topological spaces, computation.

If the set is finite you count the number of distinct elements in it.

If the set has infinitely many elements, and you can find a one-to-one mapping between these elements and the natural numbers, then its cardinality is Aleph-null. Incidentally, the cardinality of rational numbers is also Aleph-null.

If you can map its elements to the set of real numbers, and if the continuum hypothesis is true then the cardinality of the set is the next transfinite number, Aleph-one. Unfortunately, if the Zermelo-Fraenkel set theory is consistent then neither the continuum hypothesis nor its negation can be proven. [It is not that nobody has proved it, but worse: as Godel proved, in any consistent and not-trivial mathematical theory, there are statements that cannot be proved to be true or false.]

Ernst Zermelo died on 1953-05-21.

Ernst Zermelo was born on 1871-07-27.