🚀 go-pugleaf

On Mar 25, 12:04 pm, Albrecht <albst...@gmx.de> wrote:
> On 25 Mrz., 15:37, William Hughes <wpihug...@gmail.com> wrote:
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> > On Mar 25, 11:24 am, Albrecht <albst...@gmx.de> wrote:
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> > > On 25 Mrz., 12:19, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Mar 25, 4:30 am, Albrecht <albst...@gmx.de> wrote:
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> > > > > On 24 Mrz., 20:36, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > On Mar 24, 2:59 pm, Albrecht <albst...@gmx.de> wrote:
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> > > > > > > On 24 Mrz., 15:40, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
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> > > > > > > > In article <971970b6-b722-4f38-96cb-4aef5f17e...@b22g2000prb.googlegroups.com>,
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> > > > > > > > Albrecht  <albst...@gmx.de> wrote:
> > > > > > > > >Pi has to be the limit of the serie
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> > > > > > > > >3/1, 31/10, 314/100, 3141/1000, 31415/10000, ...
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> > > > > > > > >If you claim the existence of an irrational decimal number you claim
> > > > > > > > >the existence of the number
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> > > > > > > > >31415.../10000...
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> > > > > > > > >with infinite numerator and inifite denominator.
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> > > > > > > > One third has to be the limit of the series
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> > > > > > > >   3/10, 33/100, 333/1000, ...
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> > > > > > > > If you claim the existence of one third you claim the existence of the
> > > > > > > > number
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> > > > > > > >   33333.../100000...
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> > > > > > > > with infinite numerator and denominator.
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> > > > > > > No. The "number" 0.333...
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> > > > > > Was not mentioned by anyone.
> > > > > > It appears to have gone over your head
> > > > > > that Richard was simply replacing pi
> > > > > > by 1/3.
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> > > > > One can't simply replace pi by 1/3
> > > > > concerning the mentioned the
> > > > > aspects 'cause pi is irrational and 1/3 isn't.
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> > > > The point which continues to elude you is that you
> > > > made no use of the fact that pi is irrational.
> > > > You only made use of the fact that the decimal
> > > > expansion of pi is infinite.  In your argument
> > > > you can replace pi by *any* number that
> > > > has an infinite decimal expansion.
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> > > But in the case of rational numbers, the "infinite expansion" is only
> > > a phrase.  In effect there are only three dots. There is no infinite
> > > thing. In the case of irrational numbers, the decimal numeral is just
> > > a Fata Morgana. Actually any numeral which seemingly depicts an
> > > irrational number can only be definite with respect to the context.
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> > > Look at 3.1415.... .
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> > > Is it pi?
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> > > Or is it 3.141567891011... ?
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> > Neither, both are convenient
> > approximations.
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> No. E.g. 3.1415 is a approximation of pi, 3.1415... is, at most, a
> surrogat of pi.
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> > The formula for computing the digits
> > in the decimal expansion of pi is much
> > more complicated than the formula for computing
> > the digits in the decimal expansion of 1/3,
> > but both formulas produce an infinite string
> > of digits.
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> Nobody has to compute digits of 0.333... since 0.333... just symbolise
> 1/3 in the decimal system.
>
> Best
> Albrecht

What is the 5,121,365th digit in the decimal expansion of 1/3?
What is the 5,121,365th digit in the binary expansion of 1/3?
What is the 5,121,365th digit in the base 7 expansion of 1/3?

Having a simple way to compute it, is not the same as not needing
to compute it.
                      - William Hughes