On May 31, 5:43 pm, Bob Kolker <nowh...@nowhere.com> wrote: > chaja...@mail.com wrote: > > I have written a proof that 0.999... cannot be equal to one in the > > system of real numbers. > > Consider the sequence a\sub n = 9/10 + 9/100 + ... + 9/10^n. > > What is lim (n -> infinity) a\sub n? > > note that a\sub n = > 9/10 * (1 - (1/10)^(n+1))/(1 - 1/10) = 1 - (1/10)^(n+ 1) > > so that lim a\sub n (n -> infinity) = 1. > > got it? > > So you can throw away those thingies you wrote. They are wrong. > > Bob Kolker
I do not define 0.999... to be a limit and specifically state that I do not argue such a limit is not in fact 1. If I am offering a separate truth that has no meaning to you, okay. You cannot assert that students across the world are not taught that 0.999... is equal to one well before they are ever taught or told about limits. And then people hold discussions as to why students would resist. Gee, I wonder.