On 8 Feb, 10:15, Virgil <vir...@ligriv.com> wrote: > In article > <bed42ecd-011e-4c58-b474-03526a72c...@fv9g2000vbb.googlegroups.com>, > > > > > > > > > > JT <jonas.thornv...@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) > > so (Sum_{n = 1..oo} x/10^n = (x/10)/(1-1/10) > = (x/10)/(1 - 1/10) = 1/9 > = (x/10)/(9/10) > = x/9 > > Thus 0.333... = 3/9 = 1/3 and 0.999 = 9/9 = 1 > > > 0 was dreamed > > up by imagine that the empty bucket also was a mathematical statement. > > When one is paying for something by the bucketful, 0 buckets IS a > mathematical statement.
No there must be a language gap somewhere in your logic, 0 buckets is not a mathematical statement and it is not paying, it is free.
> > Infinity was dreamed up as the justification as a justification of the > > previous concepts. > > Actually, infinity first came up in geometry as a point where parallel > lines might meet back in Eucid's time. No infinity come far earlier when one noticed that there for N=x regardless x size always is a number that x<x+1 and one also noticed that there always a fraction such that 1/x > 1/x+1. > --
