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Topic: Matheology § 246
Replies: 246   Last Post: Apr 26, 2013 2:37 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 246
Posted: Apr 14, 2013 4:28 PM

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

> On 14 Apr., 01:53, Virgil <vir...@ligriv.com> wrote:
>

> > > > The union of the set of all FISONs is |N, but the sequence of all FISONs
> > > > does not contain |N, even though |N is its limit.

> >
> > > A) {1} U {1, 2} U {1, 2, 3} U ...
> > > C) {1}, {1} U {1, 2}, {1} U {1, 2} U {1, 2, 3}, {1} U {1, 2} U {1, 2,
> > > 3} U ...

> >
> > > The sequence C of all unions of FISONs does not contain |N?
> >
> > C is no more that the sequence of FISONs which makes it a strictly
> > increasing ordered sequence, ordered by inclusion, whose LIMIT is |N.

>
> The union of C is |N.

But |N is neither a member or a subset of C, so is not "in" C.

C is is sequence whose limit, |N or A, is not "in" C.
>
> Further:
> D = 1, 2, 3, ...
> and
> E = {1}, {2}, {3}, ...
> are also strictly increasing ordered sequences. Do they contain all
> natural numbers? I.e., can every natural number be found in D and E.
> If not, how can the union of E be |N.
> If E contains all natural numbers,

But E does not contain the set of all natural numbers, which is what it
must do in order to contain A.
> >
> > A strictly increasing infinite sequence like C cannot have its limit as
> > any one of its terms as there is always a larger term.

>
> I agree. 1, 2, 3, ... is not its limit - since there is no limit.
> "Forall n" is not the same as "From 1 to oo".
>

> >
> > > Why should
> > > it stop before reaching this goal

> >
> > It doesn't stop, but if it ever reached its limit, being a strictly
> > increasing sequence, it would then have to pass that limit.

>
> So it is. Therefore there cannot be limit, at least it cannot be
> reached.

WRONG! Even an infinite sequnce of sets, like B or C, can have a union
set.

> There is no "all n", because in the table
>
> 1
> 2, 1
> 3, 2, 1
> ...

B and C are sequences of sets, not tables. And thus being sets of sets
will have union sets.

> > A is a set which is not
> > equal to or contained in any term of sequence C, but only in C's limit,
> > which is not a member of C or a subset of C.

>
> So it must differ from all sets of the sequence C. What is that
> difference?

Among other things, each member of C is a finite set, but neither C nor
A are finite sets
>
> According to Zermelo's first and obviously most important Axiom 1 we
> have
> forall A forall C (forall X (X e A <==> X e C) ==> A = C)
> All n are in A and in C, no?

NO! all n in |N are members of A but none of them are members of either
B or of C, they are only members of members, which is a critical
difference.
> >
> > > Otherwise there should be a natural number or a FISON
> > > that is in A but not in C.

Actually no FISON is in A as a member and no natural is in C as a member.

Since a natural number and a FISON are never "in A" in the same way,
this is just another of WM's attempts to conflate being a member with
with being a subset. Those who deal with set theories honestly are
careful to distinguish between being a member and being a subset.

Wm is careful to conflate them at every opportunity.
> >
> > The only way that could be true would be if the limit of a strictly
> > increasing sequence could be a member of the sequence,

>
> Not at all!

Yes at all!
--

Date Subject Author
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 JT
4/12/13 fom
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 Virgil
4/12/13 fom
4/12/13 Virgil
4/12/13 fom
4/12/13 Virgil
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 Virgil
4/13/13 fom
4/12/13 Scott Berg
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 Virgil
4/13/13 Scott Berg
4/13/13 Virgil
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 Virgil
4/13/13 fom
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 fom
4/13/13 fom
4/13/13 fom
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 fom
4/13/13 Virgil
4/13/13 Virgil
4/13/13 fom
4/12/13 Virgil
4/12/13 David C. Ullrich
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 dan.ms.chaos@gmail.com
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 Virgil
4/14/13 mueckenh@rz.fh-augsburg.de
4/14/13 Virgil
4/12/13 dan.ms.chaos@gmail.com
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 dan.ms.chaos@gmail.com
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 Virgil
4/12/13 dan.ms.chaos@gmail.com
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 Tanu R.
4/12/13 dan.ms.chaos@gmail.com
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 Tanu R.
4/13/13 Tanu R.
4/13/13 Tanu R.
4/13/13 Tanu R.
4/13/13 Virgil
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 fom
4/13/13 Virgil
4/13/13 dan.ms.chaos@gmail.com
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 dan.ms.chaos@gmail.com
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 dan.ms.chaos@gmail.com
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 Virgil
4/14/13 mueckenh@rz.fh-augsburg.de
4/14/13 Virgil
4/13/13 Virgil
4/13/13 Bergholt Stuttley Johnson
4/13/13 Virgil
4/14/13 mueckenh@rz.fh-augsburg.de
4/14/13 Tanu R.
4/14/13 Virgil
4/12/13 Virgil
4/12/13 Virgil
4/13/13 fom
4/12/13 Virgil
4/12/13 Virgil
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 Tanu R.
4/13/13 Virgil
4/13/13 David C. Ullrich
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 fom
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 fom
4/13/13 Virgil
4/13/13 fom
4/13/13 David C. Ullrich
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 dan.ms.chaos@gmail.com
4/13/13 mueckenh@rz.fh-augsburg.de
4/13/13 Virgil
4/14/13 mueckenh@rz.fh-augsburg.de
4/14/13 Tanu R.
4/14/13 Virgil
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4/14/13 David C. Ullrich
4/14/13 mueckenh@rz.fh-augsburg.de
4/14/13 fom
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4/15/13 Virgil
4/15/13 fom
4/16/13 mueckenh@rz.fh-augsburg.de
4/16/13 Bergholt Stuttley Johnson
4/16/13 Virgil
4/14/13 Virgil
4/14/13 Virgil
4/15/13 mueckenh@rz.fh-augsburg.de
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4/15/13 Virgil
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4/16/13 fom
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4/17/13 Virgil
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4/17/13 Virgil
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4/17/13 mueckenh@rz.fh-augsburg.de
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4/17/13 mueckenh@rz.fh-augsburg.de
4/17/13 Virgil
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4/17/13 Virgil
4/17/13 Tanu R.
4/17/13 gus gassmann
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4/24/13 Virgil
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4/25/13 Tanu R.
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4/13/13 Virgil
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