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I'm not clear on the definition of sequence such that you could have one without having a description of how to produce it? Can you have a sequence of random nu
by fsckboy 3y ago
I'm not clear on the definition of sequence such that you could have one without having a description of how to produce it? Can you have a sequence of random numbers?
- rbanffy 3y agoAny representation of any irrational number will be an endless and never repeating sequence of seemingly random digits.
- kmod 3y agoI think the term of interest here is non-computable: irrational numbers can have finite kolmogorov complexity. You're kind of "begging the question" here, where you're assuming that non-computable numbers exist and then using that to show that some numbers are non-computable. You can definitely show that these things exist, but that relies on "believing" the set of axioms that you used to prove it.
- rbanffy 3y agoHow do we identify a specific non-computable number?
- kmod 3y agoThey are necessarily non-constructive existence proofs, for sure. You're not alone in some potential unease with that: https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics) https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...