On 31 May 2007 05:04:58 -0700, chajadan@mail.com wrote: > This has been a very educational evening for me. I would still like to > point out that no one has refuted my proof itself or pointed to > specific error or logical over-stepping it may contain.
There is nothing to refute. I don't see a proof anywhere in that paper. Even what you call "the classic proof" is not actually a proof of anything. All you do is nitpick, which is easy to do, since "the classic proof" is quite flawed.
As has been explained several times, the infinite decimal 0.999... is naturally associated with an infinite sum 9/10 + 9/10^2 + 9/10^3 + ... = sum_{k=1}^oo 9/10^k. The partial sums of this series form a Cauchy sequence. The real numbers, being a complete metric space, have the property that every Cauchy sequence converges to a real number. Thus, 0.999... is certainly a real number.
If I am reading your argument correctly, this is the point in dispute. Once we have settled that 0.999... is indeed a real number, it is easy to conclude that the only real number it can possibly be is 1.
-- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit <http://www.abu-jamal-news.com/>
