[gnulinux]

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.

[jessaustin]

...only works for natural numbers...

That proof also works for the rationals with a suitable ordering. Example: 0, 1, -1, 2, -2, 1/2, -1/2, 3, -3, 1/3, -1/3, 2/3, etc....

[gnulinux]

Yes works for all enumerable set (i.e. all sets that have a bijection with natural numbers).