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Generally mathematical theorems involving real numbers, do not care about computability (except if you are a finitist https://en.m.wikipedia.org/wiki/Finitism h
by szemet 7y ago
Generally mathematical theorems involving real numbers, do not care about computability (except if you are a finitist https://en.m.wikipedia.org/wiki/Finitism https://en.m.wikipedia.org/wiki/Finitism ) ;)
On the other hand my intuition is: flipping a coin (generating next digit of a real number between 0 and 1) and then trasforming it to e.g. an exponential random variable should always take you to the point where you can decide about the ordering in countably finite coin toss, with probability one...
- lonelappde 7y agoMathematicians don't deserve the right to amaze us with counterintuitive phenomena that can only exist in abstract theory outside the physical universe. All that shows is that their mathematical structures aren't faithful to the physical reality they pretend to model.
- rhencke 7y agoA Turing machine runs on a theoretically infinitely long tape in both directions. That doesn't make the concept of a Turing machine useless.