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I think the answer is yes and no. Let's say we knew we had a normal number, say we could prove pi is normal. Then the set of sequences defined by the decimal e
by Spivak 2y ago
I think the answer is yes and no.
Let's say we knew we had a normal number, say we could prove pi is normal. Then the set of sequences defined by the decimal expansion of pi starting at the nth place for all n in the natural numbers would be uniformly random over all decimal expansions. I'm going this route because it in theory allows us to define each sequence by virtue of a single number rather than an infinite sequence of randint(0, 9). This I think would be our best case if it were possible. But you would have to select a number uniformly in the range [0, inf) which... you can't.
- danbruc 2y agoWe actual know some normal numbers [1] but they seem to all be synthetic. I would guess they have a lot of local correlation because of the way they are constructed and the comment I responded to explicitly mentioned no self-correlations - not sure what exactly that means - but it probably indicates that being a normal number is not a strong enough condition for using its digits as a sequence of random digits. [1] https://en.wikipedia.org/wiki/Normal_number#Properties_and_examples https://en.wikipedia.org/wiki/Normal_number#Properties_and_e...