From: utzoo!decvax!duke!harpo!seismo!hao!menlo70!sytek!zehntel!tektronix!tekmdp!laurir Newsgroups: net.math Title: Re: 1=/= .999... Article-I.D.: tekmdp.1735 Posted: Fri Jan 28 22:58:38 1983 Received: Thu Feb 3 02:07:37 1983 References: rocheste.522 Example consider S = 1/2 - 1/2 + 1/2 -1/2 .... . Using the arguments given by some people, I can prove that S is both 1/2 and -1/2! The "true" answer (as any calculus text will tell you) is that S = 1/4! The "true" answer (as any calculus text will tell you) is that the sequence S does not converge, and so is not "equal" to any particular number. Getting back to what is .999..., the first mistake everyone is making is: 1/9 = .111.... ! This is not true, strictly speaking. The infite series .1 + .01 + .001 + ... CONVERGES to 1/9. It is not really 1/9. Hence 9 times a number that CONVERGES to 1/9 is a number that CONVERGES 1. This is just a matter of agreeing on notation. The majority of those who are so interested in mathematical trivia that they didn't "n" this article seem to agree that ".999..." is just shorthand for inf sigma (9*10^-i) i=1 which is the limit of the sequence, which *is* a number, equal to 1. Hence, 1/9 = .111... and 1 = .999... -- Andrew Klossner (decvax!tektronix!tekmdp!laurir)