-=Dark_Angel=-, P.I.5 Jan 2005

Dear boy, you may brush your trousers until they gleam, but you can't change the fact that '(x/x/3) = 3' is a provable, non-axiomatic statement in arithmetic, and so is a theorem of arithmetic. Just because something isn't an interesting X doesn't mean it isn't an X.

Also, why are you suddenly waffling on about Goedel? If you're talking about the incompleteness theorem, you're buncombing up the wrong pair of stilts. That says there are some true statements that aren't theorems because they aren't provable. But '(x/x/3) = 3' is provable.