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

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mueckenh@rz.fh-augsburg.de

Posts: 15,737
Registered: 1/29/05
Re: Matheology § 233
Posted: Apr 1, 2013 5:00 PM
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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!

Regards, WM



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