The assumption that something can execute an algorithm with infinitely many operations in a finite number of steps leads to contradictions. This is why most mathematicians seems to have become constructivists after Gödel and Turing. Constructive math is computation.
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Computers are machines and have obvious limitations. This is why human mind is so different, I think. Humans can come up with an idea of irrational numbers - machines cannot, I believe. IF machines rely on pure logic as they are today
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Coming up with the idea of an irrational number is very different than calculating an irrational number. The former is a matter of abductive reasoning; the latter is provably incomputable in this universe.
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I may be unaware of something but that doesn’t downgrade maths to constructivism IMO. I don’t think that infinity by definition can be achieved by a finite number of steps. And since an irrational number is an infinite fraction, of course you cannot compute it as a precise float
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I am not sure if we’re on the same page... Are you talking about Godel’s theorem of incompleteness? Like there are statements within a formal system that are not deductible by pure formal logic? And Turing theorem about finite inputs?
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