Claim:  All Numbers are Interesting

Proof:  We prove this by contradiction:  Suppose there were numbers that weren’t interesting.  Collect them all up, so that now you have the set of all numbers that aren’t interesting.  Now look at the smallest number in this set*.  What you have is the smallest number that is not interesting.  Now that’s interesting!  Whoops – we just reached a contradiction!!  (It is interesting after all).  
This contradicts our hypothesis, and thus proves the claim. (Or if you prefer, throw out that mistake, and go back and repeat the above paragraph as often as needed.)
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*In case the set is infinite, see the latest Brain Teasers, Bonus #1.