math! riddle
we really don’t have enough math here on yosefblog. what, you say? you didn’t notice? well, matt did.
here’s the issue of the day: fallacious proofs. what’s wrong with the following proof, if anything?
Theorem: Every natural number (that means counting numbers: 1, 2, 3, …) can be uniquely described by seventeen words or less in the English language
Proof: By way of contradiction, assume not every natural number can be described as such. Then (by the well-ordering principle of natural numbers) there must be a smallest such number (not “one”, “two”, etc., since they have their own words), call it x. But then x can be uniquely described as “the smallest number that cannot be uniquely described by seventeen words or less in the English language”, hence is uniquely described by 17 words, which is a contradiction.
Corollary: There are a finitely many natural numbers (since there are a finite number of English words [take OED words only], and hence a finite number of combinations of seventeen or less of those words).