From: utzoo!decvax!harpo!seismo!rocheste!FtG Newsgroups: net.math Title: 1=/= .999... Article-I.D.: rocheste.522 Posted: Thu Jan 27 09:46:35 1983 Received: Sun Jan 30 11:27:16 1983 References: hou5e.216 People are missing the whole idea in "proving" that 1=.999... . We are dealing with infinite sums here, which have very peculiar properties. 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 proof is too subtle and complex to give over the net. Clearly the manipulation of infinite sums is VERY DIFFERENT from finite ones. Infinite series cannot be capriciously added, multiplied, etc. 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. The mistake people make is in subconciously thinking that the series and its limit are the same for all practical purposes and therefore equivalent. REMEMBER: one is a series and the other is a number. Don't mix apples and oranges. Enuf said- FtG (rochester)