Insights into Mathematics | Emile Borel: Real number enthusiast or skeptic? | Sociology and Pure Mathematics | N J Wildberger @njwildberger | Uploaded 3 years ago | Updated 1 day ago
Emile Borel was a prominent French analyst and probabilist, and the founder of modern measure theory. He was also involved in the issue of "real numbers" and just what they actually are, and what it means to do arithmetic with them.

This is a first introduction to his thinking, where we discuss Borel's notion of normal numbers, and his famous, or infamous, know-it-all number.

We will be looking in further videos at his last work which is however in French: Les Nombres Inaccessibles.

The video is part of the Sociology and Pure Mathematics Playlist, where we contemplate the common ground between pure mathematics and critical social analysis.

Video Content:
00:00 Introduction to E. Borel
1:21 Skepticism about aspects of the 'theory of real numbers'
3:32 "Real numbers"- infinite decimals
12:25 Normal numbers (base 10)
19:04 Borel's know-it-all number


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