Date: Feb 23, 2013 4:15 PM Author: Virgil Subject: Re: Matheology � 222 Back to the roots In article

<62781b70-dff9-4093-85d0-ff6e5bfcbbb8@u20g2000yqj.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 22 Feb., 23:39, Virgil <vir...@ligriv.com> wrote:

> > In article

> > <6cfcca98-d4e5-475d-a4bf-168639050...@n2g2000yqg.googlegroups.com>,

> >

> >

> >

> >

> >

> > WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 22 Feb., 22:29, Virgil <vir...@ligriv.com> wrote:

> > > > In article

> > > > <c3c197e4-2161-4ecf-a84e-d479adb05...@k4g2000yqn.googlegroups.com>,

> >

> > > > WM <mueck...@rz.fh-augsburg.de> wrote:

> > > > > On 21 Feb., 21:51, Virgil <vir...@ligriv.com> wrote:

> >

> > > > > > > Or consider the union of natural numbers in a set B while there

> > > > > > > remains always one number in the intermediate reservoir A.

> >

> > > > > > > A B

> > > > > > > --> 1 -->{ }

> > > > > > > --> 2,1 -->{ }

> > > > > > > --> 2 -->1

> > > > > > > --> 3, 2 -->1

> > > > > > > --> 3 -->1, 2

> > > > > > > --> 4, 3 -->1, 2

> > > > > > > --> 4 -->1, 2, 3

> > > > > > > ...

> > > > > > > --> n -->1, 2, 3, ..., n-1

> > > > > > > --> n+1, n -->1, 2, 3, ..., n-1

> > > > > > > --> n+1 -->1, 2, 3, ..., n-1, n

> > > > > > > ...

> >

> > > > > > > One would think that never all naturals can be collected in B,

> > > > > > > since a

> > > > > > > number n can leave A not before n+1 has arrived.

> >

> > > > > > > Of course this shows that ZF with its set of all natural numbers

> > > > > > > is

> > > > > > > contradicted.

> >

> > > > > > WM's A and B are not sets but sequences of sets, so if WM wants to

> > > > > > consider a limit to any such sequences, he must first define what

> > > > > > he

> > > > > > means by such a limit, as there is no universal definition for

> > > > > > "the"

> > > > > > limit of a sequence of sets.

> >

> > > > > By definition of A we know it is never empty.

> >

> > > > There is no such thing as an "A" but only an infinite sequence of

> > > > differing A's, indexable by the infinite set of natural numbers,

> >

> > > In any case there is never an A = { }.

> > > Therefore similarly there is never a B = |N.

> >

> > There is never an A or a B which is a subset of |N either, though their

> > members are subsets of |N.

>

> You are in error.

> The set A_1 = {1} is a subset of |N.

But A_1 is merely a member of the sequence A, and is not A itself.

> The set B_1 = { } is a subset of |N

But B_1 is merely a term of sequence B and not equal to B.

SO it is WM who is in error by trying to make A stand for two different

things at once, and B stand for two different things at once.

WM's A and B can only stand for the whole of a sequence or for one term

in that sequence but not for both simultaneously, as he is trying to

make them do.

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