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Topic: Matheology § 288
Replies: 160   Last Post: Jun 21, 2013 8:42 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 288
Posted: Jun 19, 2013 10:05 AM

On 19 Jun., 15:29, "Julio Di Egidio" <ju...@diegidio.name> wrote:
> "fom" <fomJ...@nyms.net> wrote in message
>
> news:C6KdnZCccIjltVzMnZ2dnUVZ_t6dnZ2d@giganews.com...> On 6/18/2013 10:05 PM, Julio Di Egidio wrote:
>
> <snipped>
>

> >> I cannot tell for sure what apoorv had in mind, but he mentioned
> >> ordinals and I have tried to present what seems to me a pretty
> >> reasonable, simple reading and approach.  We are given that a diagonal
> >> side has order type w+1, we also assume (not stated) that we shall use
> >> comparable "machinery" when determining the base side.

>
> > And I did that.  He said nothing concerning the partitioning of
> > the third side.  So, the question is not well-construed.

>
> I do not agree, to me the question is rather underspecified.  Anyway, I'd
> propose we do not really bother too much about apoorv's "original
> intention": I had misinterpreted initially, I now see that he presented a
> finite triangle, but it's the infinite case that is interesting, the idea
> that the "triangle" is "equilateral" in the finite is obviously correct.
>

> > The geometry of construction has nothing to do with
>
> > 1 1 1 1 ... 1 1 1 1
>
> > if that sequence is put in correspondence with an ordinal.
>
> I think there is a sense in which the geometry of construction is essential
> to the mathematical analysis: I will elaborate on this in a separate post.
> Here I just note that apoorv has never written "111...111", i.e. no "..." in
> the mathematical sense, his triangle was in fact finite.  Then, I simply
> assume that we are given a sequence of finite triangles and we ask ourselves
> what is the (simplest) limit triangle, i.e. the limit of the sequence, and
> whether it remains true or not that all sides have the same order type (a
> fortiori, cardinality), i.e. whether the infinite "triangle" remains
> "equilateral", as our geometric intuition seems to suggest.
>

> >> As to my ruminations on dissymmetries, you describe the usual
> >> construction a la von Neumann, where lambda = [0, lambda), but my
> >> questions where about a kind of dissymmetry, then about constructions
> >> where lambda = [1, lambda]. Do these exist?  Does the question even make
> >> sense?

>
> > chuckle...
>
> > I do not know if they exist in some recognized mathematical
> > context.

>
> It would be great if anyone could at list give a glimpse at what would be
> impacted, if anything, by using the second approach.  In fact, despite the
> two intervals look of a different kind, in practice I am only seeing a
> rearrangement of symbols involved, i.e. nothing really substantial.
>

> > "Numbers count themselves"
>
> I will elaborate, in fact rewrite the whole thing, in a separate post.
> (Most probably, this will be later tonight.)
>

> > But, I formulated the construction specifically when considering
> > what WM had been posting.

>
> > I do not think that is what you have in mind.
>
> Honestly, I concur with WM et al. that there is something *wrong* with the
> standard view, of logic as of math as of many more things: another story is
> that I just occasionally see anything useful or even just coherent in what
> he presents.

The see this:

Every term of the sequence of sets is lacking infinitely many natural
numbers, since the n-th term has only n numbers.

1
1, 2
1, 2, 3
...

However, every term F(n) is the union of all preceding terms and {n}.
So we have infinitely many unions (as many terms as unions, if the
first term is the "union" of {1}) and a strictly increasing sequence
of sets.

These infinitely many unions do not manage to complete |N. Since the
limit of a strictly increasing sequence is not contained in the terms
of the sequence.

But if, in a last step, the union of all these deficient terms is
done, then there is |N - like Aphrodite born from the foam of the sea.

A strange misbelief.

Regards, WM

Date Subject Author
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Virgil
6/16/13 apoorv
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 apoorv
6/16/13 Virgil
6/16/13 apoorv
6/17/13 Virgil
6/17/13 apoorv
6/17/13 Virgil
6/17/13 Tanu R.
6/17/13 Virgil
6/17/13 fom
6/16/13 FredJeffries@gmail.com
6/16/13 apoorv
6/16/13 apoorv
6/17/13 FredJeffries@gmail.com
6/17/13 Virgil
6/17/13 FredJeffries@gmail.com
6/18/13 LudovicoVan
6/18/13 mueckenh@rz.fh-augsburg.de
6/18/13 Virgil
6/18/13 LudovicoVan
6/18/13 Tucsondrew@me.com
6/18/13 LudovicoVan
6/18/13 Tucsondrew@me.com
6/18/13 mueckenh@rz.fh-augsburg.de
6/18/13 Tucsondrew@me.com
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Tucsondrew@me.com
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Tucsondrew@me.com
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
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6/18/13 fom
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6/18/13 LudovicoVan
6/18/13 fom
6/19/13 LudovicoVan
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Virgil
6/19/13 LudovicoVan
6/19/13 fom
6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 mueckenh@rz.fh-augsburg.de
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6/20/13 mueckenh@rz.fh-augsburg.de
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6/20/13 mueckenh@rz.fh-augsburg.de
6/20/13 LudovicoVan
6/20/13 Virgil
6/20/13 Virgil
6/20/13 FredJeffries@gmail.com
6/20/13 LudovicoVan
6/21/13 LudovicoVan
6/21/13 LudovicoVan
6/20/13 FredJeffries@gmail.com
6/20/13 Virgil
6/20/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/14/13 Virgil
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 Virgil
6/15/13 Tanu R.
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 LudovicoVan
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Tanu R.
6/14/13 Virgil
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Bergholt Stuttley Johnson
6/14/13 Virgil
6/14/13 Tucsondrew@me.com
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Tanu R.
6/15/13 Bergholt Stuttley Johnson
6/14/13 Virgil
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
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6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 Virgil
6/17/13 mueckenh@rz.fh-augsburg.de
6/17/13 Virgil
6/17/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 fom
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/16/13 fom
6/16/13 Virgil
6/16/13 fom
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/17/13 mueckenh@rz.fh-augsburg.de
6/17/13 Virgil
6/16/13 Virgil
6/16/13 mueckenh@rz.fh-augsburg.de
6/16/13 Virgil
6/15/13 Tanu R.