From: The Higgs bozo Date: 2008-10-28T04:48:13+09:00 Subject: Re: float equality Matthew Moss wrote: >> Totally off-topic, but has any one figured out exactly why 1/9 >> (0.111...) plus 8/9 (0.888...) is 1 instead of 0.999... :-) > > Ummm... because 1/9 + 8/9 == (1 + 8)/9 == 9/9 == 1 ? > > And... because 0.999... == 1? > > x = 0.999... > 10x = 9.999... > (10x - x) = 9.999... - 0.999... > 9x = 9 > x = 1 While your answer is correct, you cannot subtract infinities as shown in your proof. Look at this: x == 1 - 1 + 1 - 1 + 1 - 1 + 1 - ... x == 1 - 1 + 1 - 1 + 1 - 1 + ... ---------------------------------------- 2x == 1 + 0 + 0 + 0 + 0 + 0 + 0 + ... x == 0.5 Does x == 0.5? No, because x was never a number in the first place because the given series does not converge. Your proof appears to work because you've already assumed 0.99999... converges, but that is what you are trying to prove. P.S. Euler thought the answer was x == 0.5. -- Posted via http://www.ruby-forum.com/.