In it, Wildberger introduces the difficulties of arithmetic with rational numbers that are too often glossed over.

Confess: have you ever seen a proof that the arithmetic for rational numbers is well-defined and the laws of arithmetic hold for them?
Discuss what you think the next video is going to be about. Clearly the negative fractions are yet to be defined but I think he means something else. Perhaps it's that the condition a/b=c/d is difficult to check in practice?
https://www.youtube.com/watch?v=p8MyvTULOWQ