🚀 go-pugleaf

On Mar 25, 11:24 am, Albrecht <albst...@gmx.de> wrote:
> On 25 Mrz., 12:19, William Hughes <wpihug...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>
> > On Mar 25, 4:30 am, Albrecht <albst...@gmx.de> wrote:
>
> > > On 24 Mrz., 20:36, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > On Mar 24, 2:59 pm, Albrecht <albst...@gmx.de> wrote:
>
> > > > > On 24 Mrz., 15:40, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
>
> > > > > > In article <971970b6-b722-4f38-96cb-4aef5f17e...@b22g2000prb.googlegroups.com>,
>
> > > > > > Albrecht  <albst...@gmx.de> wrote:
> > > > > > >Pi has to be the limit of the serie
>
> > > > > > >3/1, 31/10, 314/100, 3141/1000, 31415/10000, ...
>
> > > > > > >If you claim the existence of an irrational decimal number you claim
> > > > > > >the existence of the number
>
> > > > > > >31415.../10000...
>
> > > > > > >with infinite numerator and inifite denominator.
>
> > > > > > One third has to be the limit of the series
>
> > > > > >   3/10, 33/100, 333/1000, ...
>
> > > > > > If you claim the existence of one third you claim the existence of the
> > > > > > number
>
> > > > > >   33333.../100000...
>
> > > > > > with infinite numerator and denominator.
>
> > > > > No. The "number" 0.333...
>
> > > > Was not mentioned by anyone.
> > > > It appears to have gone over your head
> > > > that Richard was simply replacing pi
> > > > by 1/3.
>
> > > One can't simply replace pi by 1/3
> > > concerning the mentioned the
> > > aspects 'cause pi is irrational and 1/3 isn't.
>
> > 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... ?
>

Neither, both are convenient
approximations.

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.

                  - William Hughes
>