We're going to start our discussion of set theory with some definitions and basic properties, most of which will probably be familiar already. The last lecture on indexed sets and partitions may be less familiar. If you've already had an introduction to set theory, you can safely skim these lectures except possibly the last one.
Video Lectures
We're going to start our discussion of sets with some basic definitions and two different notations: the roster form and the set-builder form. (lecture slides)
There is no general way to describe one set as being greater or smaller than another. Instead, we talk about whether or not one set is a subset of or contained in another. (lecture slides)
Where the subsets that we discussed in the last lecture describe a relationship between two sets, set operations like union and intersection are tools we can use to combine two sets to create a new one. (lecture slides)
In this lecture, we're going to extend the ideas of union and intersection we discussed in the last lecture from something that operates on a single pair of sets to something that works on a larger collection of sets. (lecture slides)
