Set theory

In the following, we will be going through some fundamental aspects of set theory, the mathematical study of sets. Modern set theory is a very abstract field, and to make matters more confusing, set theory is usually formulated using a formal language of logic. And in turn, formal languages of logic are specified, both syntactically and semantically, through the use of set theory. Thus, there is a chicken-or-the-egg scenario going on. To steer clear of these issues, we will be explaining set theory in plain English terms. This approach is usually called ‘naive set theory’, to distinguish it from ‘axiomatic set theory’, something we will not be covering here.