Clearly he's a Socratic finitist. He doesn't accept mathematical induction so he's not sure whether there's a biggest number, but he's also not confident that there isn't.
Raises some puzzling questions about his acceptance of the incompleteness theorem, though.
Assume that there is a largest prime number. Take all the prime numbers, multiply them together, and add 1. Call that number N. Now N must be prime, because when you divide it by any prime number, you get 1. But now we have a prime number that's larger than the largest prime number. Contradiction
I mean, he literally could have just typed the enquoted phrase into a search engine (I just tried it), and the first result is Euclid's theorem with proofs.
There isn't even an intuitionist argument to be made here. Euler's proof is constructive...
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Raises some puzzling questions about his acceptance of the incompleteness theorem, though.
There isn't even an intuitionist argument to be made here. Euler's proof is constructive...