Infinity is a slippery topic. The work done by Georg Cantor at the beginning of the twentieth century showed that our intuitive idea of size relationships breaks down when you get to this size. In this section, we're going to see some of his basic results about the relative size of the integers, rational numbers and real numbers.

# Video Lectures

Now that we have one-to-one correspondences to work with, we can define the cardinality or size of a set then use those correspondences to define when two sets have the same cardinality.

In this lecture, we're going to look at some very non-intuitive results about different sets that all fall into the countable category. (lecture slides)

We're going to finish our discussion of sets by seeing how there are actually different sizes of infinity. (lecture slides)