In article <email@example.com>, WM <firstname.lastname@example.org> wrote: > Am Montag, 9. Dezember 2013 18:59:11 UTC+1 schrieb wpih...@gmail.com: > > To understand where WM is coming from one must note > > that for WM the statement > > for all n in N, p(n) is not true > > does not imply > > there is no n in N such that p(n) is true, > > but only that > > one cannot find an n in N such that p(n) is true. > > So for WM: > > If L is a constructable list of constructable 0/1 lists > > then there is a constructable 0/1 list, y, such that one cannot > > find a n in N with y the nth element of L. > > Most people would then argue, if n existed then we could find it, > > so the fact that we cannot find it means that n does not exist. > > WM does not agree with the last step. > And I can tell you why: > For every rational p/q we can find a digit where it differs from the > antidiagonal d. > But what means "every rational"?
In English, it means there are absolutely no rationals for which the statement following is not true. What it means in WM-ese is irrelevant.
> p/q belongs to a finite set of rationals > with a sum = <(p+q). p/q has finitely many predecessors but is followed by > infinitely many rationals p'/q' with p'+ q' being finite but larger than p + > q.
What does it mean for p/q to belong to a "finite" set of rationals with sum <= p+ q? What finite set?
OUTSIDE of WM's wild weird world of WMytheology, for any given rational p/q there are infinitely many others, p'/q', with p' + q' <= p + q. --