Suppose that there are finitely many natural number for some maximum natural number M. Since there finitely many numbers, this finite amount M of numbers may be described by sentences in the English dictionary, composed of permutations of the N words in the dictionary, containing say, 20 words or fewer.

By way of contradiction, suppose that the natural numbers are indeed unbounded and there is always some natural number which cannot be described by permutations of the N words in the dictionary consisting of

20 words or fewer. Call the least such number of this type L. However, one may then describe this least number L by the designation "The least such number not describable in 20 words or less through permutations of the N words in the dictionary." This is a contradiction - hence the natural numbers are indeed finite.