On May 31, 1:40 am, Virgil <vir...@comcast.net> wrote: > In article <1180599668.636261.130...@z28g2000prd.googlegroups.com>, > > chaja...@mail.com wrote: > > > > Fantastic, if you say that 0.999.. is not a real number, > > > > then clearly it is not equal to 1, since 1 is a real number. > > > > Unfortunately 0.999... is a real number defined by: > > > > 0.9999...= lim_{n -> oo} [ 9^{-1} + 9^{-2} +.... + 9^{-n}]. > > > > Ciao > > > > Karl >
I do agree that lim_{n -> oo} [ 9*10^{-1} + 9*10^{-2} +.... + 9*10^{- n}] = 1 if we limit our result to real numbers. Otherwise the limit would be 0.999... and not 1.
