What is the smallest positive integer that cannot be defined in less than twenty-five syllables?

(In reply to re(5): Tentative solution REVISED (Paradoxes) by Penny)

>>Let K be defined as "the smallest positive integer that cannot be defined in less than twenty-five syllables". I am afraid that sentence just defined K in 24 syllables. Ergo, there is no such positive integer. Awesome logical powers, huh ?

 

I really should stop replying to my own puzzles, but I'll put in one more little thing.

You've given the first half of the paradox. It only becomes interesting later. Have you just proved that there is no such thing as a least positive integer only definable in 25 syllables or more ("Ergo, there is no such positive integer.")? So are there any numbers only definable in 25 syllables or more??

There are an infinite number of integers, and only a finite number of sentences less then 25 syllables long.

But can any set of positive integers exist without a least member? 

Posted by Sam on 2004-04-15 19:17:58