Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 8,833
Registered: 1/6/11
Re: Matheology � 233
Posted: Apr 1, 2013 8:06 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
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.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.