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Topic: Matheology § 233
Replies: 20   Last Post: Apr 4, 2013 10:16 AM

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: Matheology � 233
Posted: Apr 1, 2013 8:06 PM
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In article
<b87e674d-d8ba-44ff-9f6c-3274dd76d006@a14g2000vbm.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 1 Apr., 17:05, William Hughes <wpihug...@gmail.com> wrote:
> > On Mar 27, 8:55 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >

> > > Matheology § 233
> >
> > > The set of all termination decimals is a subset of Q. If the set of
> > > all terminating decimals of the unit interval is arranged as set of
> > > all terminating paths of the decimal tree,

> >
> > It is, of course, impossible to write this out
> > (there number of terminating decimals is infinite).

>
> Nevertheless Cantor has given a finite formula to construct the list
> of all rationals between 0 and 1. From that formula we can find every
> entry and the anti-diagonal up to every digit d_n. From that we can
> easily prove that for every FIS d_1, d_2, ..., d_n of d there are
> infinitely many rationals with the same FISs. For every finite number
> n - and there are no other lines than such enumerated with a finite
> number!


But as there is no end to the set/list of natural/finite numbers, there
is also no end to the set/list of such lines.
--





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