Almost all numbers are normal! [English subtitles]

For non-mathematicians, this might sound pretty silly. The video explains what the sentence means and it also proves it - it's actually a famous theorem by Émile Borel. The proof shown here, based on an idea by Felix Hausdorff, is particularly simple and has been kind of forgotten since it was first published in 1914. But a lot of questions remain open. Nobody knows, for example, whether numbers like pi or e are normal...
The article mentioned in the video: doi.org/10.100...
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00:00 Introduction
03:37 Requirements
05:18 "almost all"
12:08 "normal"
22:32 Hausdorff's proof