🚀 go-pugleaf

On 25 Mrz., 12:19, William Hughes <wpihug...@gmail.com> wrote:
> 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.
>

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.

Look at 3.1415.... .

Is it pi?

Or is it 3.141567891011... ?

Who knows.

Best
Albrecht