The smallest uninteresting number

This isn't a paradox. It's simply a proof that all natural numbers are interesting, if we accept the premises. We shouldn't accept the premises, because there really is a real paradox lurking around the corner, but this isn't it.

The paradox occurs when we replace "natural number" by "ordinal". Then the same line of reasoning demonstrates that all ordinals must be interesting. But surely there can only be countably many interesting ordinals! (Because "interesting" is really code for "definable".) Which shows what the real problem in the premises were -- we failed to distinguish between definable in some particular theory and definability in the meta-theory.

See: http://en.wikipedia.org/wiki/Berry_paradox

Theorem: All natural numbers are boring.

Proof (by contradiction): Assume the set of non-boring natural numbers is nonempty, so it must have a smallest element. Call it x. So what? yawn

QED

2013 is sort of interesting - first year with non-duplicate digits since 1987

Perhaps this is the point of the original article, but couldn't one say that the actual "smallest uninteresting number" is actually the second smallest uninteresting number? The first smallest uninteresting number is only interesting by virtue of being otherwise uninteresting, but once we have a second number that is only interesting by virtue of being uninteresting, it's no longer a novelty to be uninteresting. So it's legitimately uninteresting.

Uh, the smallest uninteresting number is clearly 14.

relevant: http://www.njohnston.ca/2009/06/11630-is-the-first-uninteres...