 
Summary: Chapter 2
Basic Set Theory
A set is a Many that allows itself to
be thought of as a One.
 Georg Cantor
This chapter introduces set theory, mathematical in
duction, and formalizes the notion of mathematical
functions. The material is mostly elementary. For
those of you new to abstract mathematics elementary
does not mean simple (though much of the material
is fairly simple). Rather, elementary means that the
material requires very little previous education to un
derstand it. Elementary material can be quite chal
lenging and some of the material in this chapter, if
not exactly rocket science, may require that you ad
just you point of view to understand it. The single
most powerful technique in mathematics is to adjust
your point of view until the problem you are trying
to solve becomes simple.
Another point at which this material may diverge
