Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: Matheology § 288
Posted: Jun 18, 2013 11:41 PM
 Plain Text Reply

On 6/18/2013 10:05 PM, Julio Di Egidio wrote:
> "fom" <fomJUNK@nyms.net> wrote in message
> news:l9CdnVddyNhtl1zMnZ2dnUVZ_jKdnZ2d@giganews.com...

>> On 6/18/2013 1:38 PM, Julio Di Egidio wrote:
>>> "Julio Di Egidio" <julio@diegidio.name> wrote in message
>>> news:kppqpg\$div\$1@dont-email.me...

> <snipped>
>

>>>> Consider this:
>>>>
>>>> 1-> 1
>>>> 2-> 12
>>>> 3-> 123
>>>> ...
>>>> n-> 123...n
>>>> ...
>>>> ___
>>>> w-> 123...n...___w
>>>>
>>>> The order type of the w-th entry is again w+1.
>>>>
>>>> So, the "triangle" is "equilateral", at every step as in the limit.
>>>>
>>>> There just seems to be a sort of dissymmetry, so that the n-th entry
>>>> has order type n but the w-th entry has order type w+1.

>>
>> The omega-th entry is the union of its predecessors
>> as is typical of its definition as a limit ordinal.
>>
>> The successor of the omega-th entry takes omega as an
>> element and has order type omega+1.
>>
>> Your ">>___" is the omega-th entry.

>
> Nope, the "___" indicates that we get to the w-th entry via a limit,
> it's not itself the w-th entry. The w-th entry is the limit entry, a
> specific ordinal.
>

Correct. That is why it is the omega-th entry.

The least ordinal in which omega appears as an object
is omega+1. When you use the name 'omega' you are
already in omega+1 or beyond.

>> You should consider the possibility that apoorv's
>> question is not well-construed.

> <snip>
>
> 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. The
fact that a set can be well-ordered does not mean that some
particular construction is definitive enough to specify a
particular well-order. All that can be said is that the
initial segment and the terminal segment appear to be
organized according to the succession of homogeneous symbols.
Further, the construction suggests a countably infinite
cardinality. So, absent any partitioning criteria, one
has alpha+n where alpha is any countable limit ordinal and
n is a finite ordinal.

1) countably infinite
2) initial segment given as a succession of homogeneous symbols
3) terminal segment given as a succession of homogeneous symbols

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.

> And I am unclear if you'd at least agree concede (beside the ruminations
> that have followed) that the "triangle" I describe is "equilateral",
> i.e. its side and base have (can have) the same order type.
>

>> This is why your omega-th entry is in a set with order
>> type omega+1.

>
> 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.

They do correspond with one interpretation of WM's theory
of monotone inclusive marks.

Suppose a number is a choice function on its initial segment:

lambda(<1, ..., lambda>)=lambda

This is how I make sense out of a statement such as
that made by Albrecht:

"Numbers count themselves"

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

I do not think that is what you have in mind.

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
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/20/13 Virgil
6/19/13 Virgil
6/19/13 Virgil
6/18/13 Virgil
6/18/13 fom
6/18/13 fom
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
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 Virgil
6/20/13 Virgil
6/20/13 FredJeffries@gmail.com
6/20/13 LudovicoVan
6/20/13 Ralf Bader
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
6/16/13 Virgil
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.

© The Math Forum at NCTM 1994-2018. All Rights Reserved.