On 5 Feb., 12:17, William Hughes <wpihug...@gmail.com> wrote: > On Feb 5, 10:38 am, WM <mueck...@rz.fh-augsburg.de> wrote: > <snip> > > > So "there is no list of X" is > > true for every potentially infinite set. > > And so it goes. Now there is no list > of |N.
Now? Why should there ever have been a complete list, that means a complete sequence, that means all terms with all their indices which are all natural numbers which do not exist? > > So ends this round. It has > taken 100 posts to get WM to > admit that different potentially > infinite sets have different > listability.
Where had I conceded the complete existence of a list?
> It would take another > 100 posts to get him to admit > that he admitted it. > > We now know > that the potentially infinite > series 0.111... > > is not a single line of the list > > 0.1000... > 0.11000... > 0.111000... > ...
And we know that there is no line of the list that contains the potentially infinite sequence of natural numbers or up to which this is contained in the list. > > More importantly, we have learned that > we can use induction to show "every" > and that "every n -> P(n)" is equivalent > to "there is no m such that ~P(m)" > So we do not need to resort to "all" > to show something does not exist.
Of course, that is true. For instance we can show that no list exists, that contains, as indices, all natural numbers.