Here is a slightly more rigorous version of yesterday’s theorem.
Theorem. Every natural number can be unambiguously described in 14 words or less.
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.
