From: utzoo!watmath!cbostrum
Newsgroups: net.math
Title: no more point nine repeated please
Article-I.D.: watmath.4433
Posted: Fri Jan 28 17:42:34 1983
Received: Sat Jan 29 02:31:25 1983

all of this discussion about whether .999... = 1 is getting very irritating.
or perhaps it should be encouraging: a good demonstration that even people
ignorant of basic mathematics can effectively use computers.
grade nine proofs of the form "x=.9999... so 10*x=9.999... so 9*x=9 so x=1
so .999...=1" are simply not valid, for one thing. they are exactly the
same as "x=1+2+4+8... so 2*x=2+4+8+16... so 2*x-1=1 so x=1 so 1=infinity".
the point is that .999... is really an infinite sum, and the regular grade
nine addition does not work on all sums. it is well known how certain
types of sum are given values; this happens when the sequence of partial
sums has a limit (which is a simple but deep concept that allows us to
extend the definition of sum to include .999...). once this is done it 
becomes a trivial fact that .999...=1. now you may wish to define infinite
sums in some other way, thinking you know better than all those who have come
before you with strong intuitions, but at least be aware of what they have done
and why...