Virgil
Posts:
6,972
Registered:
1/6/11
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Re: Matheology � 246
Posted:
Apr 17, 2013 4:24 PM
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In article
<e299dff9-3db1-4d8b-ab0e-152394a69ff8@y2g2000vbe.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 17 Apr., 21:33, Virgil <vir...@ligriv.com> wrote:
>
> > > Is there any number of A that is not in at least one line?
> >
> > The set A in not "in" any one line so the set A is not in B.
>
> I did not ask about the set A, because it will turn out that there is
> no such set, if one is willing to accept that nothing of the set
> remains, after all its elements have been removed.
On that basis, no set can exist.
But as set theories do exist, perhaps removing all the elements from a
set does not mean that the original set did not exist.
Nicht wahr?
> >
> > > So we have an identity. There is no actually infinite line in B, so
> > > there is no actually infinite sequence A.
> >
> > At least not as a term of B.
>
> So it is. But it is trivially true that every element of A together
> with all its predecessors is in a line.
True but irrelevant.
To say that some subsets of one set are subsets of another does not make
all of them subsets of the other, and A is neither a subset nor a member
of B.
>
> The argument is similar to: (A < B & B < C) ==> (A < C), well-known
> and often applied in mathematics.
It is not similar enough
>
> > While WM claims that there is no set A,
>
> I don't claim it. I prove it.
WM has not proved it yet!
At least not with any arguemnt valid outside of his hideaway from logic,
Wolkenmuekenheim.
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