Virgil
Posts:
4,491
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Jan 29, 2013 5:58 PM
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In article
<4a622e7d-ac62-4208-b6ee-223d47b7039d@k4g2000yqn.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 29 Jan., 14:27, William Hughes <wpihug...@gmail.com> wrote:
> > On Jan 29, 12:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >
> > > On 29 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > To summarize
> >
> > > > For every natural number, n, the antidiagonal,d, of a list L
> > > > is not equal to the nth line of L
> >
> > > > A statement WM has made.
> >
> > > > A) For every natural number n, P(n) is true.
> > > > implies
> > > > B) There does not exist a natural number n such that P(n) is
> > > > false.
> >
> > > > A statement WM has made.
> >
> > > > There does not exist a natural number n such that d is
> > > > equal to the nth line of L
> >
> > > > A statement WM disputes
> >
> > > I do not dispute this statement (as I erroneously had said yesterday,
> > > when being in a hurry). I dispute that this statement implies the
> > > statement:
> > > d is not in one of all lines of the infinite list L
> >
> > It does, however, imply that d is not
> > of the the lines of the infinite list L.
>
> Here we have again the ambivalence required for set theory. No, your
> statement is incorrect if "infinite" is used in the sense of completed
> or actual, i.e., in the only sense that would allow for set theoretic
> cardinality.
Set theoretic cardinality is defined by existence or non-existence of
surjections from one set to another. And outside of WMYTHEOLOGY all
sets, even non-finite ones, are actual.
>
> >
> > > and, hence, cannot
> > > be used to argue that cardinality is increased.
> > > (The reson is that "all" is maeningless here.)
> >
> > > What about C1, C2, C3?
> >
> > I neither know nor care.-
>
> You should. In the case of all terminating decimals, for instance, C4
> is obviously wrong.
Since your C4 is clearly not one of C1,C2 or C3, why should it make any
of them relevant to anything except the idiocy of WMYTHEOLOGY ?
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