That doesn't work because real numbers are not enumerable, so you cannot induce over them. That joke "proof" only works for natural numbers and goes like this:

That doesn't work because real numbers are not enumerable, so you cannot induce over them. That joke "proof" only works for natural numbers and goes like this: Theorem: all natural numbers are interesting * Base case: 0 is interesting because it is the smallest natural number, as well as the identity element of + operation. * Inductive case: Assume the theorem holds for all m, m<n. Take n. If it is not interesting, then n is the smallest non-interesting number. But that's interesting because it's the smallest such number. Therefore it cannot be non-interesting. Therefore theorem holds for n. By induction, we conclude all natural numbers are interesting. QED.