  The purpose of this paper is to outline a simple set of axioms for basic set
theory from which most fundamental facts can be derived. The key to the whole
project is a new axiom of set theory which I dubbed "The Law of Extremes". It
allows for quick proofs of basic set-theoretic identities and logical
tautologies, so it is also a good tool to aid one's memory.
  I do not assume any exposure to euclidean geometry via axioms. Only an
experience with transforming algebraic identities is required.
  The idea is to get students to do proofs right from the get-go. In
particular, I avoid entangling students in nuances of logic early on. Basic
facts of logic are derived from set theory, not the other way around.
