On May 31, 7:49 am, "Jesse F. Hughes" <j...@phiwumbda.org> wrote: > mathed...@hotmail.com.CUT writes: > > You have no idea what you're talking about! > > For those who now what it means, o.999... = 1 is a > > trivial fsct and easy to prove! > > 0.999... is NOT a real number. It is a symbol that represents an > > infinite series. An infinite series, by definition, is a sequence. > > I was with you up 'til here. > > 0.999... is a representation of a real number, in the same way that 1 > is a representation of a real number (which you suggest below). > 0.999... does not represent a series or a sequence, but rather the > limit of the sequence (equivalently, the sum of the series). > > This may seem a trivial point, but it is essential to the question at > hand. If 0.999.... is literally a sequence, then it cannot be equal > to the real number represented by 1. > > > The statement 0.999... = 1 says that the sequence represented > > by the symbol on the left CONVERGES TO the number represented by > > the symbol (numeral) "1". > > -- > "This confused and outraged many Matrix fans, who'd already spent hours > on the web explaining that man and computers could never really live > in such a state of harmony and mutual benefit." > --http://www.pointlesswasteoftime.com
Jesse I'm glad you brought this up. It is imperative people understand I am using 0.999... to be literally the series. I do this for a very important reason. I do not claim the limit of 0.999... is not one as the number of positions approaches infinity. People are taught that 0.999... is equal to 1 years before they are ever taught about limits. I am saying that the full sum of the series would never equal 1, it is less, and only the limit is equal to one. We try to teach students in early math that the series itself ~equals~ one, rather than has a limit of it. It is only this equality I refute, not the limit.