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Kind of. A constructive proof by definition means something like you can explain exactly what the number is in a finite number of bytes. The standard diagonali
by dmurray 7y ago
Kind of. A constructive proof by definition means something like you can explain exactly what the number is in a finite number of bytes.
The standard diagonalization argument is a constructive proof, identifying a specific number. Normally a constructive proof is preferable. But with a bit of hand waving you can make it into a non-constructive proof that there are "unknowable" numbers that cannot be described in any finite amount of bytes.
- afiori 7y agoIn practice constructible for reals mean that you can approximate them with arbitrarily small know precision e.g. a sequence of retional number numbers q_n each no more that 1/n apart from the actual real number. The point is that such a sequence needs to be constructive in the usual sense, so there are still only a countable number of them.