In article <firstname.lastname@example.org>, WM <email@example.com> 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. --