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Yes, but the real numbers that can be computed to arbitrary precision with an algorithm are countable: this means almost all the reals contain an infinite amoun
by rnhmjoj 3y ago
Yes, but the real numbers that can be computed to arbitrary precision with an algorithm are countable: this means almost all the reals contain an infinite amount of information. The real numbers are useful to reason and construct proofs, but as far as the physical world go, only very few of them are actually meaningful.
- chongli 3y agoThe non-computable reals are also not uniquely representable. It’s this property which I think is the most reasonable explanation for why these real numbers don’t cause an information black hole.