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From: Virgil <vir...@ligriv.com>
Newsgroups: sci.logic,sci.math
Subject: Re: Matheology § 092
Organization: Anon
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Date: Sat, 11 Aug 2012 11:25:56 -0600
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In article 
<a657ca8a-4459-47bf-8e66-5c65d3aa9...@m13g2000vbd.googlegroups.com>,
 WM <mueck...@rz.fh-augsburg.de> wrote:

> On 10 Aug., 22:36, Virgil <vir...@ligriv.com> wrote:
> 
> > > By the way, why do you believe in the equinumerousity of N and Q?
> > > For every finite initial segment we have equinumerousity. Look! Over
> > > there!
> >
> > If one can construct a bijection between two sets, as has often been
> > done for N and Q, then they satisfy the standard mathematical definition
> > of equinumerousity
> 
> If equinumerousity exists by definition, then that is not enough to
> imply bijectability?

Equinumerousity between two sets is only known to exist when a bijection 
between those sets has been proved to exist.

> If I define that there are aleph_0 endpoints of the I_n and aleph_0
> endpoints of the A-B-intervals then that is not sufficient to prove
> bijectability, i.e., that they can be paired?

Proof of equinumerousity does not prove anything else.
It does not prove anything about the order properties of the sets in 
question. And it does not prove that your alleged method of reordering 
of the endpoints of the I_n is possible.
> 
> So you insist that a bijection implies equinumerousity, but that
> equinumerousity does not imply bijectability?

No I do not!
> >
> >  I prefer to
> > continue looking only at standard mathematics.
> 
> In standard mathematics the limit of the sequence 0, 0, 0, ... is 0.

Which is totally irrelevant to WM's problem, of proving his false claims.

There is no way to rearrange the endpoints of the I_n to you A-B pattern 
without destroying what the I-n were designed to do.

Among other things: 
(1) the cumulative length of the I_n intervals is less than 1/9 where 
the cumulative length of the A-B intervals is 1.
(2) the midpoints, and very likely the endpoints, of the I_n intervals 
are dense in [0,1] but the A_B interval endpoints have only one 
accumulation point.
Yet WM claims that, by a sequence of operations each moving one point at 
a time or swapping the position of two points, he can convert one to the 
other. The problem being that such an infinite process always has 
infinitely farther to go before it gets any closer to being finished.

For example, in removing the rationals, one at a time, from [0,1], what 
is left after any finite number of steps remains dense in [0,1].

Thus the proper "limit", if any, would have to be a dense in [0,1].

At lest in WMytheology.

> 
> Regards, WM
--