Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 233
Posted:
Apr 1, 2013 8:06 PM


In article <b87e674dd8ba44ff9f6c3274dd76d006@a14g2000vbm.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 1 Apr., 17:05, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 27, 8:55 am, WM <mueck...@rz.fhaugsburg.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 antidiagonal 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. 

