Excellent video by Dr. Wildberger explaining why concept of "real numbers" is rotten.
I second his call to research the sociology and history of these ideas, so we can put mathematics on sounder foundations.
YouTube Pure mathematics relies on a fake arithmetic | Sociology and Pure Mathematics | N J Wildberger Number systems are at the heart of mathematics --- and have been for at least 4000 years. The Egyptians' had a base 10 system that used fractions, albeit n...