```Date: Jan 29, 2013 4:18 AM
Author: William Hughes
Subject: Re: Matheology § 203

On Jan 29, 10:09 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 29 Jan., 09:54, William Hughes <wpihug...@gmail.com> wrote:>>>>>>>>>> > On Jan 29, 9:33 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > "All" and "every" in impredicative statements about infinite sets.>> > > Consider the following statements:>> > > A) For every natural number n, P(n) is true.> > > B) There does not exist a natural number n such that P(n) is false.> > > C) For all natural numbers P is true.>> > > A implies B but A does not imply C.>> > Which is the point.  Even though A> > does not imply C we still have> > A implies B.>> > Let  L be a list> >      d the antidiagonal of L> >      P(n),  d does not equal the nth line of L>> > We have (A)>> >    For every natural number n, P(n) is true.>> > This implies (B)>> >   There does not exist a natural number n> >   such that P(n) is false.>> > In other words, there is no line of L that> > is equal to d.>> And how can C be correct nevertheless? Because "For all" is> contradictory.   B: There is no line of L that is equal to ddoes not imply   C: For all n, line n is not equal to d.B correct does not mean "C correct nevertheless"
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