If you take any number you can think of, any integer whatsoever, count the number of letters it takes to write it out fully (with or without any 'and's you may need), then take THAT number and repeat the procedure infinitely, what number (or numbers) does this strange series converge to? Is there a unique solution?
Let's face it, this won't be a challenge. But here's an extra thing or two for you. Do you know if this series converges in every language? If the series converges, what number does it converge to? Do they have a unique solution? Can you tell of any language(s) in which does this series not converge?
Note: What if you converted this series into cardinal numbers instead (34 = thirty fourth [12 letters] then 12 = etc.)? How many possible convergence values are there in English or any other language you know?
(In reply to ordinal (other than english)
Actually these are cardinal numbers: one, two, three, ... ; it's first, second, etc. that are orginal. Also, the pdf linked to misspells the French quatre as quatra, (though that doesn't affect the letter count).
1. Also called orÆdinal nuÆmeral. any of the numbers that express degree, quality, or position in a series, as first, second, and third (distinguished from cardinal number).
1. Also called carÆdinal nuÆmeral. any of the numbers that express amount, as one, two, three, etc. (distinguished from ordinal number).
Posted by Charlie
on 2006-09-10 12:02:33