From: utzoo!decvax!harpo!ihnp4!iwlc7!dfz Newsgroups: net.math Title: Re: 1 != .999... Article-I.D.: iwlc7.133 Posted: Thu Jan 27 14:19:54 1983 Received: Sun Jan 30 07:40:47 1983 Reply-To: dfz@iwlc7.UUCP (David F. Ziffer) References: ihlpb.270 Recently there appeared here a refutation of the idea that .999... = 1. The argument suggested that 1 = 0.999... + 0.000...1; my answer to the author was that the figure 0.000...1 was in itself a contradiction, since the dots between the last zero and the one represent an infinite number of digits, yet the figure implies that it ends in a one followed by no digits. There has now appeared another argument in a similar vein, claiming that one is the sum of the "infinitely largest part of one" and the "infinitely smallest part of one". This has merely transformed the argument into a question of whether the "infinitely smallest part of one" is zero or not (I will contend that it is). For example, the infinitely smallest number "terminating" in the digit one might be expressed as 1 / ( 10 ^ infinity ) since there are an infinity number of zeros preceding the one. The number expressed above is exactly zero.