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Topic: Another AC anomaly?
Replies: 280   Last Post: Dec 27, 2009 3:53 PM

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Virgil

Posts: 870
Registered: 7/27/09
Re: Another AC anomaly?
Posted: Dec 3, 2009 3:21 PM
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In article
<27aee2d6-5966-4b62-a026-fea13e0bad6c@h2g2000vbd.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 3 Dez., 13:52, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > In article
> > <0c635f53-f5c4-4320-8825-de05f021a...@m3g2000yqf.googlegroups.com> WM
> > <mueck...@rz.fh-augsburg.de> writes:
> >  > On 2 Dez., 16:27, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> >  > > Limit cardinality is confusing because it can either mean the
> > cardinality
> >  > > of the limit set or the limit of the cardinalities.
> >  >
> >  > If the limit set is "assumed" by the sequence of sets, if for instance
> >  > N is given by unioning all naturla numbers, then tghe limit set has to
> >  > have the limit cardinality.
> >
> > The limit set is not necessarily "assumed" by the sequence of sets (if by
> > that you mean that there is a set in the sequence that is equal to the
> > limit set, if you mean something else I do not understand it at all).  When
> > you mean with your statement about N:
> >      N = union{n is natural} {n}
> > then that is not a limit.  Check the definitions about it.

>
> It is a limit. That is independent from any definition.


Every mathemtical "limit" notion has to be defined, as there is no
ur-limit notion which is universal in mathematics.

Of course, what goes on in Wolkenmuekenheim is largely irrelevant to
mathematics.

> > So below is your argument:
> >
> >  > If you want to prove that the determinant of a matrix M with not
> >  > ecclusively linear independent rows is det(M) = 0, you go two ways:
> >  > You multiply a row of the matrix M by 0, and you empty a row of M by
> >  > elementary operations which do not change the determinant. Then you
> >  > have proved that the original matrix M has the determinant 0.
> >
> > So you argue that each matrix has determinant 0?  If not what do you
> > mean with that?
> >
> >  > Same holds for cardinals of sets. You form a set by unioning its
> >  > elements, resulting in the complete set.
> >
> > You can not unite the elements if the elements are not sets in themselves
> > and when the elements are sets, the union of the elements is different
> > from the original set.  Consider:
> >    A = {{a, b}, {b, c}, {c, d}}
> > uniting the elements gives:
> >    B = {a, b, c, d}
> > quite different.

>
> Not at all different with respect to being a limit process.


Quite different in mathematics, at least outside of Wolkenmuekenheim.
> >
> >  >                                          This cannot change the
> >  > connection between cardinal number and set during the whole process of
> >  > formation. For every step the cardinal number and the number of
> >  > elements of the set are equal.
> >
> > What do you mean with "every step"?  Uniting sets is a single step
> > operation.
> >

>
> No. Uniting two sets or singlets or elements is a single-step
> operation.
> Uniting infinitely many sets or singlets or elements is a limit
> process.


Not when using the Peano axioms.
>
> >  > Same holds for the cylinder. Its contents is
> >  >   {1}, {1}, {1}, {1} , ...
> >  > and that is not different from
> >  >   {1}, {2}, {3}, {4} , ...
> >  > as you can see by renaming the elements.
> >
> > I do not understand this at all.

>
> I see. You seem to share that fate with most so-called matematicians.

> >
> >  > I think that this answers all the questions contained in the
> >  > following. Therefore I extinguish it.
> >
> > No.  I asked you for a mathematical definition of "actual infinity" and you
> > told me that it was "completed infinity".  Next I asked you for a
> > mathematical
> > definition of "completed infinity" but you have not given an answer.  So I
> > still do not know what either "actual infinity" or "completed infinity"
> > are.

>
> Both are nonsense.


Then don't base your arguments on them.

And neither is needed in any version of set theory outside of
Wolkenmuekenheim.

> The axiom of infinity is adefinition of actual infinity.
> "There *exists* a set such that ..."
> Without that axiom there is only potential infinity, namely Peano
> arithmetic.


Without that axiom, or something like it, there is no Peano arithmetic.


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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
anonymous.rubbertube@yahoo.com
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil

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