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?

The series of spelled out integers will converge on one of the integers where the value of the number is equal to its length in letters, or it may converge not to a single number but a cycle through a series of numbers:

Convergence:
English: 4 = four

Italian: 3 = tre

German & Dutch: 4 = vier

Chinese: 3 = san

Greek *(in Greek letters): 
      5 = pi epsilon ^{with tanos} nu tau epsilon

Swedish: 3 = tre
              4 = fyra

Japanese: 2 = ni
               3 = san

Hindi: 2 = do
         4 = char
         5 = panch

Cyclic:
Latin: 4,8 = quattuor, octo 

French: 4,6,3,5 = quartre, six, trois, cinq

Catalan: 3,4,6 = tres, quatro, sis

Polish: 4,6,5 =  Cztery, Sześć, Pięć

Convergence/Cyclic:
Spanish & Portuguese: 5 = cinco
                               4,6 = cuatro, seis

Russian *(in Cyrillic letters): 
      3 = te er i  
     11 = o de i en en a de tse a te [soft sign]
     4,6,5 = che ie te yeru er ie , sha ie es te [soft sign] ,
                    pe ya te [soft sign]

Edited on September 11, 2006, 5:45 am

Posted by Dej Mar on 2006-09-10 23:56:41