In article <386d5767-1eb5-4910-811f-8daf7aef60d3@g16g2000vbf.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 18 Feb., 14:11, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 18, 1:38 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 18 Feb., 11:53, William Hughes <wpihug...@gmail.com> wrote: > > > > > > Is there a potentially infinite sequence, > > > > x, such that the nth FIS of x consists of > > > > n 1's > > > > > Yes, of course > > > > Let y be a potentially infinite process > > There are no processes with respect to numbers and lists. They are > existing or are not existing.
Then ther is no such thing a potentially infinite, as that would require existence of a process that does not end.
> Potential infinity with respect to natural numbers means: You can > consider every natural number you like. There is no upper threshold. > So name any set of natural numbers - except using naive and > couterfactual "all" of some kind like "all prime numbers" or all "even > numbers".
So for any set of naturals you can name, there is a process for finding a superset of that set, even in Wolkenmuekenheim.
If one cannot ever have something true for ALL natural numbers, how can one ever use inductive proofs?
> Now realize what potential infinity means: There are no processes in > above list.
It also means that induction can never conclude that anything is true for all natural numbers.
In Wolkenmuekenheim one cannot say "For all n, if n is a natural then n+1 is a natural." because on cannot ever say "For all n"
> We simply write some lines and stop at some point.
Thus WM can never prove that anything by induction. --
