Functions aren't really a discrete math topic, *per se*, but they're a useful tool that show up in pracitally every branch of mathematics. In this lecture, we're going to go over the specific concepts that we need to talk about how to compare the sizes of sets in the next section.

# Video Lectures

Functions aren't really a discrete math topic in their own right but they’re so generally useful that they show up in practically every branch of mathematics in one form or another. We're not going to go into their analysis in any great detail rather just focusing on the specific properties that are going to be useful to use in analyzing the relationships between sets. (lecture slides)

Before we get into the two relationships we really need to analyze the sizes of sets, we have a few more details to add: equality of functions, well-defined functions and how functions operate on sets. (lecture slides)

The idea of a function being one-to-one is something you’'ve probably seen before. It’'s an important part of determining whether or not a function has an inverse. We're going to start off with the technical definition which may be a little more precise that what you'’ve seen before. (lecture slides)

Onto functions, functions where the codomain and the range are the same, are the last new type of function we need to talk about methods for comparing the sizes of two sets. (lecture slides)

Before we move back to our discussion of set theory, there are a few special functions you need to be aware and that you've probabily seen before in algebra or pre-calculus classes: the identity function, inverse functions and composite functions. (lecture slides)