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> Since there are only a countable number of formulas, there are only countably many definable reals It always seemed like it should matter that the constructa
by bandrami 2y ago
> Since there are only a countable number of formulas, there are only countably many definable reals
It always seemed like it should matter that the constructable formula strings include strings that define multiple numbers (e.g. "three; also pi squared") which at least seems like it should be aleph one rather than aleph nought, but smarter people than me assure me it doesn't work that way for (reasons)
- EGreg 2y agoConsider this: https://en.wikipedia.org/wiki/Berry_paradox https://en.wikipedia.org/wiki/Berry_paradox
- NooneAtAll3 2y agothat redundancy will only decrease the number of definables, no? and countable infinity is already the smallest one, so you can't get smaller