Lecture 7 - Cantor's Diagonalization Argument, More Topics

Yesterday we talked about ways to show $\mathbb{R}$ is uncountable. In some regards, there's another way to argue $\mathbb{R}$ is uncountable without any properties of $\mathbb{R}$. We can talk about Cantor's Diagonalization Argument, which show this in a nicer way. You should compare it with the argument for the countability of $\mathbb{Q}$ to see where the argument fails for that.

We then talked about the Power Set, which helped prove Cantor's Theorem. This theorem helps us more formally define Cardinality.