Virgil
Posts:
4,674
Registered:
1/6/11
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Re: Proof 0.999... is not equal to one.
Posted:
Feb 8, 2013 5:23 PM
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In article
<be5fcd81-26ea-4a03-b223-32ea2d4d17e0@fw24g2000vbb.googlegroups.com>,
JT <jonas.thornvall@gmail.com> wrote:
> 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.
When paying for things, the statement that you have nothing to pay for
is just as relevant as that you have something to pay for.
>
> > > 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.
For positive x it is true that 1/x > 1/(x+1)
but for all non-zero x it is false that 1/x > 1/x+1
and for x = 0, 1/x is undefined.
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