From: Matthew Moss Date: 2008-10-28T05:56:57+09:00 Subject: Re: float equality On Oct 27, 2008, at 2:48 PM, The Higgs bozo wrote: > 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. But 0.999... does converge, while 1 - 1 + 1 - 1 +... does not.