Every natural number can be unambiguously described in 14 words or less.
28 September 2009
Unbelievable? Proof copied from http://komplexify.com/epsilon/2009/04/05/on-describing-integers/:
Proof. Suppose there is some natural number which cannot be unambiguously described in fourteen words or less. Then there must be a smallest such number. Let's call it n.
But now n is "the smallest natural number that cannot be unambiguously described in fourteen words or less." This is a complete and unambiguous description of n in fourteen words, contradicting the fact that n was supposed not to have such a description!
Therefore, all natural numbers can be unambiguously described in fourteen words or less. Q.E.D.
:-)
