Here’s the slides from the Introduction to Logic class. Also, some videos discussing some paradox with infinity.
The first one gives a proof of Cantor’s famous proof that there’s different types of infinity (proof done by contradiction) :
The second one (a bit long, but very interesting) concern another famous theorem, the Banach-Tarski Theorem. Really nice video showing the link between this result and Cantor’s Theorem :
The last one is also on the Banach-Tarski Theorem (also a bit long) but explain more how this theorem is dependent on the Axiom of choice. Unfortunately this video is in French but very well done :
Enjoy!
Find the solutions of the exercises here.