Proof of the Schroeder-Bernstein theorem

This is a lecture that I have recorded for my MATH 3350 (Intro to Math Proof) course where I present the classic proof of the Scroeder-Bernstein theorem. What is fascinating about this proof is that, although the result itself is intuitively obvious and self-evident, the proof is insanely complicated. Consequently it is hard not to share it with you.

Compare with the wikipedia "proof" that makes even less sense to me.
https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem

Lecture notes for the course:
https://faculty.utrgv.edu/eleftherios.gkioulekas/Teaching/LectureNotes/LuluBooks/IntroMathProof.pdf