>>6 A set of elements S is said to be infinite if the elements of a proper subset S' can be put into one-to-one correspondence with the elements of S. An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite.
Pure mathematics is not a science (a good thing because science is for dumb plebs who don't understand platonic philosophy) and is like applied philosophy (which shows how theoretical philosophy really is and theoretical is always a good thing)