In article <bed42ecd-011e-4c58-b474-03526a72cfe5@fv9g2000vbb.googlegroups.com>, JT <jonas.thornvall@gmail.com> wrote:
> On 8 Feb, 03:54, 1treePetrifiedForestLane <Space...@hotmail.com> > wrote: > > like I said, N years ago; > > you are interpolating the value of the real number, > > 1.0000..., with some finitistic interpretation > > of the "pre _The Decimals_ by Simon Stevin [pen name]" concept > > of numbertheorists, essentially Roman God-am numerals; > > good for you! > > Numbers are finite by nature, if you working with some nonefinite > concept of noneterminating string you are not working with a number, > not for Pi not for 1/0 not for 0.333.. not for 0999... not for inf. > These are not mathematical entities, they are concept dreamed up by > the human mind, 0.333... and 0.999 was dreamed up because partition of > bases is inadequate way to describe fractional parts.
Actually they were "dreamed up" as geometric series, Sum_(n = 1..oo) 3/10^n = 3*(Sum_{n = 1..oo} 1/10^n) and Sum_(n = 1..oo) 9/10^n = 9*(Sum_{n = 1..oo} 1/10^n), where, for all r with -1 < r < 1, one has Sum_(n = 1..oo) r^n = r/(1-r)
