4 ms·
It's a fun personal discovery in mathematics when you realise there are different degrees of infinites.
by dia80 6y ago
It's a fun personal discovery in mathematics when you realise there are different degrees of infinites.
- daviddaviddavid 6y agoTotally agree! When I was in school, I took a logic class that used Boolos & Jeffrey's "Computability and Logic", which is a really great book. Chapter 2 is a very clear presentation of Cantor's diagonalization proof that there exist uncountable sets. It blew my mind.
- deleted 6y ago[deleted]
- ogogmad 6y agoThe fact that all countable subsets of the real numbers have Lebesgue measure zero (as proved in the video) implies that the real numbers are uncountable. Otherwise the real numbers would have Lebesgue measure zero, which is absurd. This approach to proving R uncountable is carried out more formally here (proof A.3): https://link.springer.com/content/pdf/bbm%3A978-1-4614-8854-5%2F1.pdf https://link.springer.com/content/pdf/bbm%3A978-1-4614-8854-...
- shitgoose 6y agoSpeaking of absurd. I remember when I found out that Cantor set (uncountable) has measure 0, my mind was blown. No wonder Cantor ended up in an institution (as I heard).