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Déjà vu

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  Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-03 07:24 -0800
    Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-03 18:47 +0100
      Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-03 11:27 -0800
      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-04 03:34 -0800
        Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 06:34 -0800
    Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-05 00:17 +0800
      Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 11:14 -0800
        Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-05 20:39 +0800
          Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:53 -0800
            Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-07 17:55 +0800
              Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:07 -0800
                Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:13 -0800
                  Re: Déjà vu Simon Roberts <retenshun@gmail.com> - 2017-01-07 04:03 -0800
                  Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-08 00:54 +0800
                    Re: 4-figure tables and geometry "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-08 00:58 +0800
                      Re: 4-figure tables and geometry Apollyon <adravirgo@gmail.com> - 2017-01-07 09:01 -0800
                      Re: 4-figure tables and geometry "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 12:25 -0800
                        Re: 4-figure tables and geometry Peter Percival <peterxpercival@hotmail.com> - 2017-01-07 20:36 +0000
                          Re: 4-figure tables and geometry "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 12:41 -0800
                            Re: 4-figure tables and geometry bursejan@gmail.com - 2017-01-07 16:04 -0800
                      Re: 4-figure tables and geometry Robert Wessel <robertwessel2@yahoo.com> - 2017-01-07 23:30 -0600
                        Re: 4-figure tables and geometry "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-08 21:52 +0800
                          Re: 4-figure tables and geometry "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-10 22:06 +0800
              Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-07 04:44 -0800
      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-04 14:12 -0800
        Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 14:50 -0800
          Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:18 -0800
        Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 15:01 -0800
          Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:19 -0800
            Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 02:21 -0800
              Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:41 -0800
                Re: Déjà vu bursejan@gmail.com - 2017-01-05 02:47 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 03:00 -0800
                  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 04:08 -0800
                    Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:26 -0800
                    My GeoPosition is a point at infinity Vinicius Claudino Ferraz <boralaemcasa@gmail.com> - 2017-01-05 16:24 -0800
            Re: Déjà vu bursejan@gmail.com - 2017-01-05 02:36 -0800
              Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:50 -0800
                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 03:02 -0800
                  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 04:09 -0800
                    Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:28 -0800
                      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 09:00 -0800
                        Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 09:15 -0800
                          Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 11:20 -0800
                            Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-05 21:53 +0100
                              vu uv datum abu.kuanysh05@gmail.com - 2017-01-05 13:06 -0800
                            Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 16:33 -0800
                            Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 18:41 -0800
                              Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 02:20 -0800
                                Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 12:45 +0100
                                  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 05:30 -0800
                                    Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 15:59 +0100
                                      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 09:11 -0800
                                        Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 18:54 +0100
                                          Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 13:25 -0800
                                            Re: Déjà vu Vinicius Claudino Ferraz <boralaemcasa@gmail.com> - 2017-01-06 13:40 -0800
                                            Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 23:19 +0100
                                              Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 14:37 -0800
                                                Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:34 -0800
                                                  Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:36 -0800
                                                  Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 12:21 -0800
                                                    Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 18:41 -0800
                                    Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-06 10:09 -0500
                                      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 09:10 -0800
                                        Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-06 09:14 -0800
                                        Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-06 18:19 -0500
                                          Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 16:53 -0800
                                          Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 01:02 -0800
                                            Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:01 -0800
                                            Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-07 10:20 -0500
                                              Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 09:22 -0800
                                                Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 09:51 -0800
                                                Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 09:52 -0800
                                                  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 10:12 -0800
                                                    Re: Déjà vu bursejan@gmail.com - 2017-01-07 10:21 -0800
                                                    Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 10:24 -0800
                                                      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 10:57 -0800
                                                        Re: Déjà vu genmailus@gmail.com - 2017-01-07 11:05 -0800
                                                          Re: Déjà vu bursejan@gmail.com - 2017-01-07 11:32 -0800
                                                            Re: Déjà vu bursejan@gmail.com - 2017-01-07 11:47 -0800
                                                        Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 11:15 -0800
                                                    Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 17:21 -0800
                                                      Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-07 20:48 -0800
                                                      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-08 01:36 -0800
                                                      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-08 01:38 -0800
                                                        Re: Déjà vu bursejan@gmail.com - 2017-01-08 03:04 -0800
                                                        Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-08 13:27 +0100
                                                Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 10:01 -0800
                                                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 12:34 -0500
                                                  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-09 10:08 -0800
                                                    Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 17:18 -0500
                                                      Re: Déjà vu genmailus@gmail.com - 2017-01-09 14:28 -0800
                                                        Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 17:55 -0500
                                                          Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-09 17:12 -0800
                                                            Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 20:55 -0500
                                                              Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-09 18:08 -0800
                                                                Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-09 23:08 -0800
                                                                  Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 10:55 -0500
                                                          Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 05:13 -0800
                                                            Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 09:49 -0500
                                                              Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 07:44 -0800
                                                                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 11:45 -0500
                                                                  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 09:51 -0800
                                                                  Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 10:33 -0800
                                                                    Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 10:35 -0800
                                                                      Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 13:00 -0800
                                                              Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 11:05 -0800
                                                                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 18:08 -0500
                                                                  Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 17:25 -0800
                                                                    Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 01:48 -0500
                                                                      Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 23:24 -0800
                                                                      Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 00:34 -0800
                                                                        Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 11:26 -0500
                                                                          Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 08:55 -0800
                                                                            Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 12:13 -0500
                                                                              Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:20 -0800
                                                                              Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:22 -0800
                                                                                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:23 -0800
                                                                                Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 13:11 -0500
                                                                                  Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:26 -0800
                                                                                    Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 13:42 -0500
                                                                                      Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:50 -0800
                                                                                      Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:58 -0800
                                                                                      Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 11:01 -0800
                                                                                        Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 11:03 -0800
                                                                                          Re: Déjà vu bursejan@gmail.com - 2017-01-11 11:11 -0800
                                                      Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 00:03 -0800
                                                        Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 10:21 -0500
                                  Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 07:29 -0800
                                Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 07:27 -0800
                                  Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 09:17 -0800
                                    Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 09:35 -0800
                                    Re: Déjà vu bursejan@gmail.com - 2017-01-06 13:54 -0800
                Re: Déjà vu bursejan@gmail.com - 2017-01-05 03:13 -0800
        Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-05 08:46 -0800
        Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-05 08:51 -0800
          Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:53 -0800

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#359963

On Saturday, January 7, 2017 at 7:58:01 PM UTC+1, WM wrote:
> Am Samstag, 7. Januar 2017 19:24:22 UTC+1 schrieb Me:
> > On Saturday, January 7, 2017 at 7:13:03 PM UTC+1, WM wrote:
> > > Am Samstag, 7. Januar 2017 18:53:01 UTC+1 schrieb Me:
> > > >
> > > > Hence it seems that your "Mückenheim-limit" is restricted to a) sequences of
> > > > closed intervals that b) are "inclusion monotonic" and where c) the limits
> > > > of the sequences of the endpoints [...] exists in each case. 
> > > > 
> > > > Great. So I fail to see any benefit of your Mückenheim-limit in 
> > > > mathematics.
> > > >
> > > It would easen the understanding of the following difficult fact [...]
> > >
> > If you say so. [...]
> > 
> > And where did you apply your Mückenheim-limit here?
> >
> The infinite but not transfinite union of the rows is comparable with (0, 1]. 
> In this case however set theory claims a limit that would be analogous to 
> [0, 1], 

I donj't think so.

> namely the limit of the rows, a set with aleph_0 elements.

So you didn't *apply* it (your Mückenheim-limit)?

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#359997

On Saturday, January 7, 2017 at 7:13:03 PM UTC+1, WM wrote:

> There are infinit sets which are not transfinite.

Oh pleeze, Mr. Mückenheim, define /infinite set/ and /transfinite set/ in the language of modern set theory. Thank you very much!

http://www.imagesbuddy.com/images/128/2014/01/please-many-times-graphic.jpg

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#360012

On Saturday, 7 January 2017 17:22:03 UTC-8, Me  wrote:
> On Saturday, January 7, 2017 at 7:13:03 PM UTC+1, WM wrote:
> 
> > There are infinit sets which are not transfinite.
> 
> Oh pleeze, Mr. Mückenheim, define /infinite set/ and /transfinite set/ in the language of modern set theory. Thank you very much!
> 
> http://www.imagesbuddy.com/images/128/2014/01/please-many-times-graphic.jpg

Here, let me help:

Infinite set: noun denoting bullshit

Transfinite set:  noun denoting more bullshit

Hope this helps? :-)

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#360016

Am Sonntag, 8. Januar 2017 02:22:03 UTC+1 schrieb Me:
> On Saturday, January 7, 2017 at 7:13:03 PM UTC+1, WM wrote:
> 
> > There are infinit sets which are not transfinite.
> 
> Oh pleeze, Mr. Mückenheim, define /infinite set/ and /transfinite set/ in the language of modern set theory. Thank you very much!

Modern set theory is too primitive a theory to be able to distinguish both. It is rather based on the incapability to distinguish potential and actual infinity. People even seem to be proud on this stupidity. And outside modern set theory the distinction is irrelevant, since there is nothing transfinite outside.

Regards, WM

Regards, WM

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#360017

Am Sonntag, 8. Januar 2017 02:22:03 UTC+1 schrieb Me:
> On Saturday, January 7, 2017 at 7:13:03 PM UTC+1, WM wrote:
> 
> > There are infinit sets which are not transfinite.
> 
> Oh pleeze, Mr. Mückenheim, define /infinite set/ and /transfinite set/ in the language of modern set theory. Thank you very much!

Modern set theory is too primitive a theory to be able to distinguish both. It is rather based on the incapability to distinguish potential and actual infinity. People even seem to be proud on this lack of acumen. And outside modern set theory the distinction is irrelevant, since there is nothing transfinite outside.

Regards, WM

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#360023

If you are an expert in potential vs actual sets, and
you have also recently said, that you are firm that
proofs can be communicated. 

How do we communicate a result such as MVT? How can
the recipient of proof message be sure that the theorem
he received works for the his function,

when the sender of the proof message didn't know which
function the recipient will use? What kind of infinity
is involved here?

Am Sonntag, 8. Januar 2017 10:38:41 UTC+1 schrieb WM:
> Am Sonntag, 8. Januar 2017 02:22:03 UTC+1 schrieb Me:
> > On Saturday, January 7, 2017 at 7:13:03 PM UTC+1, WM wrote:
> > 
> > > There are infinit sets which are not transfinite.
> > 
> > Oh pleeze, Mr. Mückenheim, define /infinite set/ and /transfinite set/ in the language of modern set theory. Thank you very much!
> 
> Modern set theory is too primitive a theory to be able to distinguish both. It is rather based on the incapability to distinguish potential and actual infinity. People even seem to be proud on this lack of acumen. And outside modern set theory the distinction is irrelevant, since there is nothing transfinite outside.
> 
> Regards, WM

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#360029

On 08.01.2017 10:38, WM wrote:
> Am Sonntag, 8. Januar 2017 02:22:03 UTC+1 schrieb Me:
>> On Saturday, January 7, 2017 at 7:13:03 PM UTC+1, WM wrote:
>>
>>> There are infinit sets which are not transfinite.
>>
>> Oh pleeze, Mr. Mückenheim, define /infinite set/ and /transfinite set/ in the language of modern set theory. Thank you very much!
>
> Modern set theory is too primitive a theory to be able to distinguish both. It is rather based on the incapability to distinguish potential and actual infinity. People even seem to be proud on this lack of acumen. And outside modern set theory the distinction is irrelevant, since there is nothing transfinite outside.

Bravo, Mücke!
Everbody will agree: Your distinction is irrelevant in "Set Theory" and 
irrelevant outside "Set Theory".
But what is it that is neither inside nor outside? Why, that must be 
Muckmeatics, there where there is no there there.

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#359945

On Saturday, January 7, 2017 at 6:22:16 PM UTC+1, WM wrote:
> Am Samstag, 7. Januar 2017 16:20:22 UTC+1 schrieb Jim Burns:
> >
> > Do you invent a new definition of limit for each question?
> >
> No, I invented this limit only for the very special case of inclusion 
> monotonic seqeuences of real intervals, in order to have another, simpler 
> example where union and limit [your WM_limit, that is --Me] differ in set
> theory.

*lol* A fascinating approach. On the other hand, when we apply the usual set-theoretic limit we still have 

      lim A_n = U{A_n : n e IN)

if (A_n) is a "inclusion monotonic" (=nondecreasing) sequence of sets.

See:
https://en.wikipedia.org/wiki/Set-theoretic_limit#Monotone_sequences

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#360290

On 1/7/2017 12:22 PM, WM wrote:
> Am Samstag, 7. Januar 2017 16:20:22 UTC+1
>  schrieb Jim Burns:

>> You replace the limit set of a sequence of sets with
>> with a set with endpoints equal to the limits of
>> of the sequences of endpoints of the set sequence.
>
> Yes. lim [a_, b_n] = [lim a_, lim b_n].

You struggle over what a particular letter-sequence means,
"limit". But if I use a different letter-sequence, meaning
what I meant before, your argument has no footing. It falls
off the pier and flops around in the bay, irrelevant.

Define the _least upper bound_ of an increasing sequence
of sets A_n as a set B such that,
    for all n, A_n sub B
and
    for all sets C, if, for all n, A_n sub C, B sub C

LUB [ 0, 1 - 1/n ] = [ 0, 1 )

Is that "wrong"?

>>
>> Having changed the definition, you find that you disagree
>> with everyone else about the limit of that sequence of sets.
>
> The reason is that set theory puts union = limit,
>  which is wrong.

The least upper bound of an increasing sequence of sets
is the union of those sets.

>  But most have not comprehended that, in particular for
>  the sequence of FISONs or finite rows
> 1
> 1, 2
> 1, 2, 3
> ...
> The union is not a transfinite set, i.e.,
>  a set larger than all FISONs.

Every FISON is a proper subset of the union of all FISONs.
"Limit" or "least upper bound" is irrelevant to this.

Also, there is a mapping from the union to a
proper subset of the union, what we commonly consider
proof that the union is infinite.

Also also, this is not true of any FISON. They are
each finite.

>> Do you invent a new definition of limit for each question?
>
> No, I invented this limit only for the very special case
>  of inclusion monotonic seqeuences of real intervals,
>  in order to have another, simpler example where union
>  and limit differ in set theory.

So, you invent a new meaning for a word and any other meaning
becomes "wrong". Can anyone play this game?

Guess what "instructor" means when I refer to you, WM.

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#360300

Am Montag, 9. Januar 2017 18:34:41 UTC+1 schrieb Jim Burns:
> On 1/7/2017 12:22 PM, WM wrote:
> > Am Samstag, 7. Januar 2017 16:20:22 UTC+1
> >  schrieb Jim Burns:
> 
> >> You replace the limit set of a sequence of sets with
> >> with a set with endpoints equal to the limits of
> >> of the sequences of endpoints of the set sequence.
> >
> > Yes. lim [a_, b_n] = [lim a_, lim b_n].
> 
> You struggle over what a particular letter-sequence means,

No, I show that two different meanings are confused in set theory.
> 
> Define the _least upper bound_ of an increasing sequence
> of sets A_n as a set B such that,
>     for all n, A_n sub B
> and
>     for all sets C, if, for all n, A_n sub C, B sub C
> 
> LUB [ 0, 1 - 1/n ] = [ 0, 1 )
> 
> Is that "wrong"?

I do not say that one of the two limits is "wrong". I only show that there are two different limits. I do this in order to have an example easy enough to understand that the union and the analytical limit of the sequence of FISOns differ too.
> 
> > The reason is that set theory puts union = limit,
> >  which is wrong.
> 
> The least upper bound of an increasing sequence of sets
> is the union of those sets.

According to set theory the least upper bound of the sequence of FISONs is a set with cardinality aleph_0. The union of FISONs however has not cardinality aleph_0. Everybody can see this here
1
1, 2
1, 2, 3
...
The claim that all finite sets when written together in a single row yield a set that is larger than all, is simply foolish.
> 
> Every FISON is a proper subset of the union of all FISONs.

No. Since the union consists only of FISONs, it cannot surpass all.
> 
> Also, there is a mapping from the union to a
> proper subset of the union, what we commonly consider
> proof that the union is infinite.

The union is infinite, but not transfinite, i.e., not greater than all unioned sets.
> 
> Also also, this is not true of any FISON. They are
> each finite.

Of course. Their whole sequence can be defined recursively by F(n) = F(n-1) U {n}.
If there are infinitely many FISONs, then we have infinitely many such equantions and hence infinitely many unions already producing all infinitely many FISONs. None has card aleph_0. A further union, number omega + 1, without any further ingerdient, cannot surpass the all existing sets, because to surpass in cardinality means to have more elements.

Regards, WM

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#360377

On 1/9/2017 1:08 PM, WM wrote:
> Am Montag, 9. Januar 2017 18:34:41 UTC+1 schrieb Jim Burns:
>> On 1/7/2017 12:22 PM, WM wrote:
>>> Am Samstag, 7. Januar 2017 16:20:22 UTC+1
>>>  schrieb Jim Burns:

>>>> You replace the limit set of a sequence of sets with
>>>> with a set with endpoints equal to the limits of
>>>> of the sequences of endpoints of the set sequence.
>>>
>>> Yes. lim [a_, b_n] = [lim a_, lim b_n].
>>
>> You struggle over what a particular letter-sequence means,
>
> No, I show that two different meanings are confused
> in set theory.

"are confused". Passive voice. "Are confused" by whom?
You introduced another definition for "limit" and
now you have confused yourself.

Here, I have an idea: use the standard definition for
the limit of an increasing sequence of sets: union.
'Bye with the confusion.

>> Define the _least upper bound_ of an increasing sequence
>> of sets A_n as a set B such that,
>>     for all n, A_n sub B
>> and
>>     for all sets C, if, for all n, A_n sub C, B sub C
>>
>> LUB [ 0, 1 - 1/n ] = [ 0, 1 )
>>
>> Is that "wrong"?
>
> I do not say that one of the two limits is "wrong".

Ah. Therefore, when you say below:
   "The reason is that set theory puts union = limit,
    which is wrong",
it looks as though what you mean by saying something and
not saying something "has been confused". Of course,
with the use of passive voice, we have no idea
who did the confusing.

>  I only show that there are two different limits.
>  I do this in order to have an example easy enough
>  to understand that the union and the analytical limit
>  of the sequence of FISOns differ too.

I see no good reason for you to have introduced your
analytical limit.

You want some contradiction to appear so that you can
argue against complete infinity. But giving some
different definition of "limit" and getting different results
is not a contradiction -- any more than pointing out
the fact that there is no x such that 2*x = 3 _in the integers_
while at the same time there is such an x _in the rationals_.

That's not to say that I can't think of less-than-good
reasons.

>>> The reason is that set theory puts union = limit,
>>>  which is wrong.
>>
>> The least upper bound of an increasing sequence of sets
>> is the union of those sets.
>
> According to set theory the least upper bound of the
>  sequence of FISONs is a set with cardinality aleph_0.
>  The union of FISONs however has not cardinality aleph_0.

The least upper bound and the union are the same set.
Apparently, it "has been confused" that the same set both
has and doesn't have the cardinality aleph_0 .

>  Everybody can see this here
> 1
> 1, 2
> 1, 2, 3
> ...
> The claim that all finite sets when written together
> in a single row yield a set that is larger than all,
> is simply foolish.

No set in an _infinite_ increasing sequence of sets
can be as large as or larger then all the sets in the sequence.
If it were, it would have to be the last set, but there is no
last set.

>> Every FISON is a proper subset of the union of all FISONs.
>
> No. Since the union consists only of FISONs,
> it cannot surpass all.

This is as false as the last time you said this.
There is no last FISON, so the union _must_
surpass all.

>> Also, there is a mapping from the union to a
>> proper subset of the union, what we commonly consider
>> proof that the union is infinite.
>
> The union is infinite, but not transfinite,
>> i.e., not greater than all unioned sets.

Why not use the same meaning for "transfinite" as
everyone else?

>> Also also, this is not true of any FISON. They are
>> each finite.
>
> Of course. Their whole sequence can be defined recursively
> by F(n) = F(n-1) U {n}.

I would agree with the "of course", but not because of
that recursion relation -- which looks remarkably similar
to the recursive definition for von Neumann ordinals.
Von Neumann ordinals have no problem with being infinite.

> If there are infinitely many FISONs,
>  then we have infinitely many such equantions and hence
>  infinitely many unions already producing all infinitely
>  many FISONs. None has card aleph_0.

I'm hoping that you don't mean "of course" all FISONs
are finite because none has card aleph_0. That isn't
a reason, it's a re-statement.

>  A further union,
>  number omega + 1, without any further ingerdient, cannot
>  surpass the all existing sets, because to surpass in
>  cardinality means to have more elements.

The cardinality of omega + 1 is the same as the cardinality
of omega.

By an interesting non-coincidence, omega + 1 has a bijection
with omega which is a proper subset of omega + 1 and this
is the definition of an infinite set. Funny how that
works out.

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#360383

On Monday, 9 January 2017 14:18:18 UTC-8, Jim Burns  wrote:
> On 1/9/2017 1:08 PM, WM wrote:
> > Am Montag, 9. Januar 2017 18:34:41 UTC+1 schrieb Jim Burns:
> >> On 1/7/2017 12:22 PM, WM wrote:
> >>> Am Samstag, 7. Januar 2017 16:20:22 UTC+1
> >>>  schrieb Jim Burns:
> 
> >>>> You replace the limit set of a sequence of sets with
> >>>> with a set with endpoints equal to the limits of
> >>>> of the sequences of endpoints of the set sequence.
> >>>
> >>> Yes. lim [a_, b_n] = [lim a_, lim b_n].
> >>
> >> You struggle over what a particular letter-sequence means,
> >
> > No, I show that two different meanings are confused
> > in set theory.
> 
> "are confused". Passive voice. "Are confused" by whom?
> You introduced another definition for "limit" and
> now you have confused yourself.
> 
> Here, I have an idea: use the standard definition for
> the limit of an increasing sequence of sets: union.
> 'Bye with the confusion.
> 
> >> Define the _least upper bound_ of an increasing sequence
> >> of sets A_n as a set B such that,
> >>     for all n, A_n sub B
> >> and
> >>     for all sets C, if, for all n, A_n sub C, B sub C
> >>
> >> LUB [ 0, 1 - 1/n ] = [ 0, 1 )
> >>
> >> Is that "wrong"?
> >
> > I do not say that one of the two limits is "wrong".
> 
> Ah. Therefore, when you say below:
>    "The reason is that set theory puts union = limit,
>     which is wrong",
> it looks as though what you mean by saying something and
> not saying something "has been confused". Of course,
> with the use of passive voice, we have no idea
> who did the confusing.
> 
> >  I only show that there are two different limits.
> >  I do this in order to have an example easy enough
> >  to understand that the union and the analytical limit
> >  of the sequence of FISOns differ too.
> 
> I see no good reason for you to have introduced your
> analytical limit.
> 
> You want some contradiction to appear so that you can
> argue against complete infinity. 

I don't think any argument is needed here because there is no such thing as complete infinity. That is an oxymoron. WM wins each time because his arguments are sound.

> But giving some
> different definition of "limit" and getting different results
> is not a contradiction -- any more than pointing out
> the fact that there is no x such that 2*x = 3 _in the integers_
> while at the same time there is such an x _in the rationals_.
> 
> That's not to say that I can't think of less-than-good
> reasons.
> 
> >>> The reason is that set theory puts union = limit,
> >>>  which is wrong.
> >>
> >> The least upper bound of an increasing sequence of sets
> >> is the union of those sets.
> >
> > According to set theory the least upper bound of the
> >  sequence of FISONs is a set with cardinality aleph_0.
> >  The union of FISONs however has not cardinality aleph_0.
> 
> The least upper bound and the union are the same set.
> Apparently, it "has been confused" that the same set both
> has and doesn't have the cardinality aleph_0 .
> 
> >  Everybody can see this here
> > 1
> > 1, 2
> > 1, 2, 3
> > ...
> > The claim that all finite sets when written together
> > in a single row yield a set that is larger than all,
> > is simply foolish.
> 
> No set in an _infinite_ increasing sequence of sets
> can be as large as or larger then all the sets in the sequence.
> If it were, it would have to be the last set, but there is no
> last set.
> 
> >> Every FISON is a proper subset of the union of all FISONs.
> >
> > No. Since the union consists only of FISONs,
> > it cannot surpass all.
> 
> This is as false as the last time you said this.
> There is no last FISON, so the union _must_
> surpass all.
> 
> >> Also, there is a mapping from the union to a
> >> proper subset of the union, what we commonly consider
> >> proof that the union is infinite.
> >
> > The union is infinite, but not transfinite,
> >> i.e., not greater than all unioned sets.
> 
> Why not use the same meaning for "transfinite" as
> everyone else?
> 
> >> Also also, this is not true of any FISON. They are
> >> each finite.
> >
> > Of course. Their whole sequence can be defined recursively
> > by F(n) = F(n-1) U {n}.
> 
> I would agree with the "of course", but not because of
> that recursion relation -- which looks remarkably similar
> to the recursive definition for von Neumann ordinals.
> Von Neumann ordinals have no problem with being infinite.
> 
> > If there are infinitely many FISONs,
> >  then we have infinitely many such equantions and hence
> >  infinitely many unions already producing all infinitely
> >  many FISONs. None has card aleph_0.
> 
> I'm hoping that you don't mean "of course" all FISONs
> are finite because none has card aleph_0. That isn't
> a reason, it's a re-statement.
> 
> >  A further union,
> >  number omega + 1, without any further ingerdient, cannot
> >  surpass the all existing sets, because to surpass in
> >  cardinality means to have more elements.
> 
> The cardinality of omega + 1 is the same as the cardinality
> of omega.
> 
> By an interesting non-coincidence, omega + 1 has a bijection
> with omega which is a proper subset of omega + 1 and this
> is the definition of an infinite set. Funny how that
> works out.

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#360390

On 1/9/2017 5:28 PM, genmailus@gmail.com wrote:
> On Monday, 9 January 2017 14:18:18 UTC-8,
> Jim Burns  wrote:

>> You want some contradiction to appear so that you can
>> argue against complete infinity.
>
> I don't think any argument is needed here because
>  there is no such thing as complete infinity.

I haven't been able to get a clear description of
the distinction between complete infinity and
potential infinity.

Suppose I have a language L that contains the term 0
and, if x is a term in L, then Sx is also a term.

Does this language have a potential infinity of terms?
Does being a potential infinity keep me from doing
something that I would usually do?

(An example of something I might do that tends to give
anti-complete-infinitarians fits is to map each
term of L to to a set of terms of L. Is this an
oxymoron?)

Does language L have a complete infinity of terms?
Would that make L an oxymoron? Does that mean L
doesn't exist? If it does, why wouldn't L exist?

(I should point out that we use languages with
features very like what L has. Do these languages
"not exist"?)


>  That is an oxymoron. WM wins each time because
>  his arguments are sound.

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#360420

On Monday, January 9, 2017 at 11:56:01 PM UTC+1, Jim Burns wrote:
> On 1/9/2017 5:28 PM, genmailus@gmail.com wrote:
> > On Monday, 9 January 2017 14:18:18 UTC-8,
> > Jim Burns  wrote:
> 
> >> You want some contradiction to appear so that you can
> >> argue against complete infinity.
> >
> > I don't think any argument is needed here because
> >  there is no such thing as complete infinity.
> 
> I haven't been able to get a clear description of
> the distinction between complete infinity and
> potential infinity.

Well, a very short intro:

"Cantor's work was well received by some of the prominent mathematicians of his day, such as Richard Dedekind. But his willingness to regard infinite sets as objects to be treated in much the same way as finite sets was bitterly attacked by others, particularly Kronecker. There was no objection to a 'potential infinity' in the form of an unending process, but an 'actual infinity' in the form of a completed infinite set was harder to accept." [H.B. Enderton: "Elements of Set Theory", Academic Press, New York (1977) p. 14f] 

You might try this:

"Potential versus Completed Infinity" by  Eric Schechter
https://math.vanderbilt.edu/schectex/courses/thereals/potential.html

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#360428

On 1/9/2017 8:12 PM, Me wrote:
> On Monday, January 9, 2017 at 11:56:01 PM UTC+1,
> Jim Burns wrote:
>> On 1/9/2017 5:28 PM, genmailus@gmail.com wrote:
>>> On Monday, 9 January 2017 14:18:18 UTC-8,
>>> Jim Burns  wrote:

>>>> You want some contradiction to appear so that you can
>>>> argue against complete infinity.
>>>
>>> I don't think any argument is needed here because
>>>  there is no such thing as complete infinity.
>>
>> I haven't been able to get a clear description of
>> the distinction between complete infinity and
>> potential infinity.
>
> Well, a very short intro:

Thank you for your help. I will look at the web page.
I bet I could find something in the Stanford
Encyclopedia, too, and maybe I will.

I don't think all that will help with my actual
complaint, though -- which I have not been at all
clear about. I apologize if you feel misled by my
lack of clarity.

I believe that there are actual concepts of potential
and actual infinity, that there was once respectable
work done in that area, and there might even be
respectable work being done today.

However, the vast majority of references to potential
and complete infinity I see here don't seem clear at all,
and -- much worse -- don't agree with each other as
to what potential vs complete infinity is. I could
(conceivably) become a renowned expert on what is
called potential infinity in the literature without
coming a step closer to being able to hold a useful
conversation with WM about what _he_ calls potential
infinity. And even if I could do that with WM, it
wouldn't help me hold a useful conversation with anyone
else about potential infinity. Or so it seems to me.

Maybe genmailus@gmail.com has the same idea as WM
has as to what "potential infinity" means. My suspicion
is, though, that finding out what the idea is that
genmailus@gmail.com is defending won't help me understand
WM.



> "Cantor's work was well received by some of the
>  prominent mathematicians of his day, such as Richard
>  Dedekind. But his willingness to regard infinite sets
>  as objects to be treated in much the same way as finite
>  sets was bitterly attacked by others, particularly
>  Kronecker. There was no objection to a 'potential
>  infinity' in the form of an unending process, but an
>  'actual infinity' in the form of a completed infinite
>  set was harder to accept." [H.B. Enderton: "Elements of
>  Set Theory", Academic Press, New York (1977) p. 14f]
>
>
> You might try this:
>
> "Potential versus Completed Infinity" by  Eric Schechter
> https://math.vanderbilt.edu/schectex/courses/thereals/potential.html
>

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#360431

On Monday, January 9, 2017 at 5:55:20 PM UTC-8, Jim Burns wrote:
> On 1/9/2017 8:12 PM, Me wrote:
> > On Monday, January 9, 2017 at 11:56:01 PM UTC+1,
> > Jim Burns wrote:
> >> On 1/9/2017 5:28 PM, genmailus@gmail.com wrote:
> >>> On Monday, 9 January 2017 14:18:18 UTC-8,
> >>> Jim Burns  wrote:
> 
> >>>> You want some contradiction to appear so that you can
> >>>> argue against complete infinity.
> >>>
> >>> I don't think any argument is needed here because
> >>>  there is no such thing as complete infinity.
> >>
> >> I haven't been able to get a clear description of
> >> the distinction between complete infinity and
> >> potential infinity.
> >
> > Well, a very short intro:
> 
> Thank you for your help. I will look at the web page.
> I bet I could find something in the Stanford
> Encyclopedia, too, and maybe I will.
> 
> I don't think all that will help with my actual
> complaint, though -- which I have not been at all
> clear about. I apologize if you feel misled by my
> lack of clarity.
> 
> I believe that there are actual concepts of potential
> and actual infinity, that there was once respectable
> work done in that area, and there might even be
> respectable work being done today.
> 
> However, the vast majority of references to potential
> and complete infinity I see here don't seem clear at all,
> and -- much worse -- don't agree with each other as
> to what potential vs complete infinity is. I could
> (conceivably) become a renowned expert on what is
> called potential infinity in the literature without
> coming a step closer to being able to hold a useful
> conversation with WM about what _he_ calls potential
> infinity. And even if I could do that with WM, it
> wouldn't help me hold a useful conversation with anyone
> else about potential infinity. Or so it seems to me.
> 
> Maybe genmailus@gmail.com has the same idea as WM
> has as to what "potential infinity" means. My suspicion
> is, though, that finding out what the idea is that
> genmailus@gmail.com is defending won't help me understand
> WM.
> 
> 
> 
> > "Cantor's work was well received by some of the
> >  prominent mathematicians of his day, such as Richard
> >  Dedekind. But his willingness to regard infinite sets
> >  as objects to be treated in much the same way as finite
> >  sets was bitterly attacked by others, particularly
> >  Kronecker. There was no objection to a 'potential
> >  infinity' in the form of an unending process, but an
> >  'actual infinity' in the form of a completed infinite
> >  set was harder to accept." [H.B. Enderton: "Elements of
> >  Set Theory", Academic Press, New York (1977) p. 14f]
> >
> >
> > You might try this:
> >
> > "Potential versus Completed Infinity" by  Eric Schechter
> > https://math.vanderbilt.edu/schectex/courses/thereals/potential.html
> >

As self-proclaimed retro-finitists, 
those closed-minded goons have 
pretty much nothing to teach 
or learn from you.  Their time 
is gone.  

(There are many a variety of 
numerical methods that provide 
closed-form solutions for various 
constrained systems that don't 
need closed-minded goon trolls, 
at all.)

Burns, you're amusing and insightful, 
you'd as well entertain your notions 
with the idea of speculating about 
the nature of the infinite (its 
nature, it's infinite).

Instead of wasting time trying to 
"understand" WM, maybe you should 
explain yourself.

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#360451

On Monday, January 9, 2017 at 6:08:55 PM UTC-8, Ross A. Finlayson wrote:
> On Monday, January 9, 2017 at 5:55:20 PM UTC-8, Jim Burns wrote:
> > On 1/9/2017 8:12 PM, Me wrote:
> > > On Monday, January 9, 2017 at 11:56:01 PM UTC+1,
> > > Jim Burns wrote:
> > >> On 1/9/2017 5:28 PM, genmailus@gmail.com wrote:
> > >>> On Monday, 9 January 2017 14:18:18 UTC-8,
> > >>> Jim Burns  wrote:
> > 
> > >>>> You want some contradiction to appear so that you can
> > >>>> argue against complete infinity.
> > >>>
> > >>> I don't think any argument is needed here because
> > >>>  there is no such thing as complete infinity.
> > >>
> > >> I haven't been able to get a clear description of
> > >> the distinction between complete infinity and
> > >> potential infinity.
> > >
> > > Well, a very short intro:
> > 
> > Thank you for your help. I will look at the web page.
> > I bet I could find something in the Stanford
> > Encyclopedia, too, and maybe I will.
> > 
> > I don't think all that will help with my actual
> > complaint, though -- which I have not been at all
> > clear about. I apologize if you feel misled by my
> > lack of clarity.
> > 
> > I believe that there are actual concepts of potential
> > and actual infinity, that there was once respectable
> > work done in that area, and there might even be
> > respectable work being done today.
> > 
> > However, the vast majority of references to potential
> > and complete infinity I see here don't seem clear at all,
> > and -- much worse -- don't agree with each other as
> > to what potential vs complete infinity is. I could
> > (conceivably) become a renowned expert on what is
> > called potential infinity in the literature without
> > coming a step closer to being able to hold a useful
> > conversation with WM about what _he_ calls potential
> > infinity. And even if I could do that with WM, it
> > wouldn't help me hold a useful conversation with anyone
> > else about potential infinity. Or so it seems to me.
> > 
> > Maybe genmailus@gmail.com has the same idea as WM
> > has as to what "potential infinity" means. My suspicion
> > is, though, that finding out what the idea is that
> > genmailus@gmail.com is defending won't help me understand
> > WM.
> > 
> > 
> > 
> > > "Cantor's work was well received by some of the
> > >  prominent mathematicians of his day, such as Richard
> > >  Dedekind. But his willingness to regard infinite sets
> > >  as objects to be treated in much the same way as finite
> > >  sets was bitterly attacked by others, particularly
> > >  Kronecker. There was no objection to a 'potential
> > >  infinity' in the form of an unending process, but an
> > >  'actual infinity' in the form of a completed infinite
> > >  set was harder to accept." [H.B. Enderton: "Elements of
> > >  Set Theory", Academic Press, New York (1977) p. 14f]
> > >
> > >
> > > You might try this:
> > >
> > > "Potential versus Completed Infinity" by  Eric Schechter
> > > https://math.vanderbilt.edu/schectex/courses/thereals/potential.html
> > >
> 
> As self-proclaimed retro-finitists, 
> those closed-minded goons have 
> pretty much nothing to teach 
> or learn from you.  Their time 
> is gone.  
> 
> (There are many a variety of 
> numerical methods that provide 
> closed-form solutions for various 
> constrained systems that don't 
> need closed-minded goon trolls, 
> at all.)
> 
> Burns, you're amusing and insightful, 
> you'd as well entertain your notions 
> with the idea of speculating about 
> the nature of the infinite (its 
> nature, it's infinite).
> 
> Instead of wasting time trying to 
> "understand" WM, maybe you should 
> explain yourself.


Burns, I hope you'll excuse me.
It's not my place to be off-putting 
(though, by now I vouch that the 
local retro-finitists are trolls, 
and don't feed the trolls, 
and starve the trolls).

I just would hope that you would 
educate us instead of wasting 
effort on the ineducable.

We might learn something.

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#360486

On 1/10/2017 2:08 AM, Ross A. Finlayson wrote:

> Burns, I hope you'll excuse me.
> It's not my place to be off-putting
> (though, by now I vouch that the
> local retro-finitists are trolls,
> and don't feed the trolls,
> and starve the trolls).
>
> I just would hope that you would
> educate us instead of wasting
> effort on the ineducable.
>
> We might learn something.

My goal in reading and posting here is no more noble than
my own amusement -- though that might be hard to see. What
amuses me might well look like hard work to many other people.

Sometimes, I respond because I _must_ . I made a comparison
recently to a piece of chalk squeaking across a blackboard.
Sometimes, I have to _stop that chalk_ .

If you learn something from my posts, then I am glad.
I sincerely thank you for your attention.

I know I learn from posting, even if I only learn what
I think about some topic. That's useful, too.

   "How can I tell what I think till I see what I say?"
   -- E.M. Forster

As for feeding the trolls, they don't seem to like
many of the dainties I offer them. I'm not going to worry
about them getting fat on what I serve them.

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#360468

On Monday, 9 January 2017 14:56:01 UTC-8, Jim Burns  wrote:
> On 1/9/2017 5:28 PM, genmailus@gmail.com wrote:
> > On Monday, 9 January 2017 14:18:18 UTC-8,
> > Jim Burns  wrote:
> 
> >> You want some contradiction to appear so that you can
> >> argue against complete infinity.
> >
> > I don't think any argument is needed here because
> >  there is no such thing as complete infinity.
> 
> I haven't been able to get a clear description of
> the distinction between complete infinity and
> potential infinity.

That is untrue. WM has given you "innumerable" explanations.

Infinity: Junk. It does not exist.

The fact that there is even discussion about potential and actual infinity just proves that infinity is such a dubious concept, it needs an adjective in an attempt to clarify its meaning.

If infinity were well defined, there would be no need for additional adjectives.

Let me make it very simple for you: there is NO definition of infinity. You asking for a definition is the same as someone telling you that you can buy bird's milk and then you asking which bird produced the milk.

Get some common sense man. You can't be that stupid. Or can you?

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#360481

Thank you for your contribution, Mr Gabriel.
You have given me an excellent example of the
sort of thing I was talking about to
Me <franz.fritschee.ff@gmail.com>

You made no attempt to clarify _what_ you were talking
about, and it's a pretty good bet that whatever
you mean (if anything) it is different from what
WM means (if anything) by the same terms.

In the face of that, whatever any actual mathematician
has to say about infinity, potential or complete,
seems pointless.

On 1/10/2017 8:13 AM, John Gabriel wrote:
> On Monday, 9 January 2017 14:56:01 UTC-8,
> Jim Burns  wrote:
>> On 1/9/2017 5:28 PM, genmailus@gmail.com wrote:
>>> On Monday, 9 January 2017 14:18:18 UTC-8,
>>> Jim Burns  wrote:

>>>> You want some contradiction to appear so that you can
>>>> argue against complete infinity.
>>>
>>> I don't think any argument is needed here because
>>>  there is no such thing as complete infinity.
>>
>> I haven't been able to get a clear description of
>> the distinction between complete infinity and
>> potential infinity.
>
> That is untrue.
>  WM has given you "innumerable" explanations.

It's more accurate to say
WM has given us innumerable "explanations".

> Infinity: Junk. It does not exist.

Perfect circles don't exist either. Welcome to mathematics.

Consider the _labels_ 0, 1, 2, 3, ...
Never mind what is getting labeled.

Is there a last label?

Suppose that we have rules for writing the next label,
which next label is none of the previous labels.
So, no label can be last.

What should we call the collection-without-last-one
of these labels?

Well, "infinite" occurs to me. But you've got your
panties in a bunch over _that word_ .

A lovely property of things-like-those-labels
is that there is a matching, one-to-one both ways,
between the collection of things and and an incomplete
part of the collection of things.
    (AKA, a bijection between the collection and a
    proper subset of the collection).

For example,
    0 --> 1
    1 --> 2
    2 --> 3
    3 --> 4
    ...

Or, another example,
    0 --> 0
    1 --> 2
    2 --> 4
    3 --> 6
    ...

So, instead of "infinite", we could make up a word,
"autosubbijectible" and call things-like-those-labels
autosubbijectible.

So, you say infinity does not exist.
Does autosubbijectibility exist?
If not, why not?

> The fact that there is even discussion about
>  potential and actual infinity just proves that infinity
>  is such a dubious concept, it needs an adjective in
>  an attempt to clarify its meaning.

I like this argument. (It's why I'm bothering to
respond this time.) It's so _useful_ ! One can prove
_anything_ with it. Just start a discussion about
something and that proves that ... uh ... something.
Anyway:

Let's talk about time machines. Hey-Oh! Time travel
must be possible. Good to know.

> If infinity were well defined, there would be no need for
>  additional adjectives.

Just like right triangles are obviously nonsense.
Good of you to point that out.

> Let me make it very simple for you:
>  there is NO definition of infinity.

You would be the fellow who doesn't know what
a definition is. So, this is kind of underwhelming.

>  You asking for a definition is the same as someone
>  telling you that you can buy bird's milk and
>  then you asking which bird produced the milk.
>
> Get some common sense man. You can't be that stupid.
>  Or can you?

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