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.