```Date: Feb 4, 2013 3:21 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 3 Feb., 23:09, William Hughes <wpihug...@gmail.com> wrote:> On Feb 3, 10:58 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>>> > On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote:>> > > > > We can say  "every line has the property that it> > > > > does not contain every initial segment of s"> > > > > There is no need to use the concept "all".>> > > > Yes, and this is the only sensible way to treat infinity.>> > > So now we have a way of saying>> > > s is not a line of L>> > > e.g.  0.111...  is not a line of>> > > 0.1000...> > > 0.11000...> > > 0.111000....> > > ...>> > > because every line, l(n),  has the property that> > > l(n) does not  contain every  initial> > > segment of 0.111...>> > But that does not exclude s from being in the list.>> It certainly excludes 0.111... from being a single line> of the list.>> So the question is now>> Can a potentially infinite list> of potentially infinite 0/1> sequences have the property that>> if s is a potentially infinite 0/1> sequence, then there is a line, g, of L> with the property that every> initial segment of s is contained in g> ?-Of course, every FIS is in a line. And every FIS contains allpreceding FIS.This list0.10.110.111...contains every FIS of 0.111... as well in the (unchanged) diagonal asin a line. Obviously the diagonal cannot have more 1' than every line.(Of course you cannot expect to define 0.111... without a last element1_omega but to find a last line g.)Regards, WM
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