Universal Set

We have seen how sets can be combined and compared, but every discussion in set theory takes place within a fixed, agreed-upon "universe" of objects. That universe is the universal set, denoted by $U$, which contains every element under consideration for a particular problem. For instance, if we are studying the set of all even numbers, the universal set might be the set of all integers. Once $U$ is fixed, every other set we talk a …