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Groups > sci.math > #602228 > unrolled thread
| Started by | Peter Peters <pp1585024@gmail.com> |
|---|---|
| First post | 2023-06-14 03:35 -0700 |
| Last post | 2023-07-05 07:48 -0700 |
| Articles | 20 on this page of 165 — 16 participants |
Back to article view | Back to sci.math
The mathematical constraints of set theory Peter Peters <pp1585024@gmail.com> - 2023-06-14 03:35 -0700
Re: The mathematical constraints of set theory Guckie <alberstein@freenet.de> - 2023-06-14 16:36 +0300
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 07:45 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 08:20 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 16:30 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 11:45 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:13 +0100
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 18:07 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 06:24 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 05:50 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-15 17:36 +0100
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 13:51 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:19 +0100
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 04:44 -0700
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 10:39 -0700
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-27 09:00 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:13 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 15:45 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-14 10:08 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:44 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 08:03 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 08:29 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-16 09:03 -0700
Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-16 13:30 -0400
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 12:08 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-17 06:26 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-17 09:18 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 05:57 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-18 07:01 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:13 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-17 10:09 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-17 10:58 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:09 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-18 09:40 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 05:05 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:15 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:22 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:38 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:40 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:24 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 09:11 -0700
Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 11:27 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 11:44 -0700
Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 12:07 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 12:12 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-20 06:43 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-20 06:53 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-19 16:47 +0100
Re: The mathematical constraints of set theory Dieter Heidorn <d.heidorn@t-online.de> - 2023-06-19 20:11 +0200
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 00:08 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:49 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:35 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:09 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:19 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 01:13 +0100
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 18:35 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 03:04 +0100
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:52 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:54 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 15:42 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-27 08:39 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 02:43 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 04:32 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 15:16 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 07:48 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 16:43 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:49 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-29 09:59 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-30 13:04 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-30 18:09 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:18 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:25 -0700
Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-30 18:53 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 16:42 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-01 10:19 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-01 14:06 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:52 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 09:48 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 10:39 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 13:45 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 14:09 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-02 14:08 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 07:01 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-03 13:09 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-04 08:33 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-04 18:43 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:50 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 10:39 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 08:45 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 13:14 -0400
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-06 06:27 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-09 06:41 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-09 07:58 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:40 -0700
Re: The mathematical constraints of set theory Tom Bola <Tom@bolamail.etc> - 2023-07-01 20:23 +0200
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 11:44 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:43 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 08:42 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 06:52 -0700
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-07-01 11:56 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:34 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 20:21 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:46 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:11 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 08:20 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:18 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 07:12 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:45 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:38 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:39 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:04 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-19 09:34 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:44 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 13:31 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:37 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:03 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:05 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:53 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:50 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-21 07:37 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:13 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 20:34 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:59 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-21 11:58 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:19 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-22 12:30 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 10:38 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 20:18 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:06 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:17 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:24 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:16 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-15 09:50 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 14:00 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:28 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:50 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-18 02:13 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:19 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 01:26 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 07:09 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 15:38 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 12:32 -0700
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-20 14:05 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-21 04:43 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:33 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:56 +0100
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-17 18:34 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-14 16:50 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-14 20:19 -0400
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 17:08 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:45 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-16 14:58 -0400
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 18:56 -0400
Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-19 08:37 -0700
Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-23 11:16 -0700
Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 00:23 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:54 -0700
Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 09:36 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-06 05:29 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-09 08:09 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:42 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 04:14 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 07:27 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 07:57 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-05 07:48 -0700
Page 4 of 9 — ← Prev page 1 2 3 [4] 5 6 7 8 9 Next page →
| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-06-27 08:39 -0700 |
| Message-ID | <1a9e81af-6176-473f-b602-b5b81b6dee4en@googlegroups.com> |
| In reply to | #603335 |
On Monday, June 26, 2023 at 10:42:30 AM UTC-4, Ben Bacarisse wrote:
> Fritz Feldhase <franz.fri...@gmail.com> writes:
>
> > On Monday, June 26, 2023 at 4:04:18 AM UTC+2, Ben Bacarisse wrote:
>
> >> but I don't think that's what he means.
> >
> > Oh really? So WHAT does "Most fractions are without index" mean in you
> > book? Huh?!
> What matters is what he means, not what I mean! What he means will vary
> from day to day and will sometimes depend on where in a circular
> argument he currently stands.
>
> I think today he is as the point where k is not a "finished" function
> but a process where, at every step, only finitely many fractions have an
> index and infinite many are without one. And in WM-land, that which is
> true ate very step is just true. I would guess that the domain and
> range are not in question today.
>
> If and when this point of view becomes untenable, the dark numbers will
> pop back and NxN will have "most" fraction dark about which inductive
> proofs can say nothing. NxN will still have infinitely many unindexed
> elements, but you won't be able to find any or even prove that there
> exist (not that the don't) because... dark.
>
> If he can be persuaded that N, and hence NxN, can have nothing in it
> other than what we say, the process view will pop back.
> > Btw. we already had this discussion in de.sci.mathematik.
> >
> > Hint: There he even denied that f(n) = n (f: IN --> IN) is a bijective
> > function from IN onto IN. Reason: There are no bijections between
> > infinite sets. ("They are not possible ") Period.
> I've also already had this discussion (more than once). For example:
>
> WM: k = (m + n - 1)(m + n - 2)/2 + m.
>
> Me: I.e. k(n,m) is a bijection from NxN to N, a fact provable by any
> student who has read your textbook. Do you agree that such a student
> could prove this fact?
>
> WM: Of course.
>
> The textbook also includes examples. Specifically it states that f(x) =
> x (where f is from N to N) is bijective.
> > Hence k is not a bijection from IN x IN --> IN, no matter what you
> > say.
> That depends on what he means by a set and by a bjection today! k is
> provably bijective or it does not exist. Take you pick.
>
> --
> Ben.
If he can't name a dark number then it does not exist.
I happen to have a system that allows their naming. For instance:
0.000...01
will never be reached by the untimely progression of 1/n.
You can even double this value:
0.000...02
and yes, you can even halve it:
0.000...00.5
and these decimal places (two of them in this instance) are considerate of aleph, but aleph has jumped into a radix form here of aleph digits, which explains how these values will never be reached in the 1/n progression. The 1/n progression is a radix one form. It is haltingly slow relative to these rapid digital forms which exhibit this other gain in terms of representation. Modern number theory ignores this detail.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-28 02:43 +0100 |
| Message-ID | <87fs6cnyzc.fsf@bsb.me.uk> |
| In reply to | #603481 |
Timothy Golden <timbandtech@gmail.com> writes: > If he can't name a dark number then it does not exist. Have you told him? If so, did he agree? > I happen to have a system that allows their naming. But can you prove they are in my set N? WM explains the things that bother him about infinite sets like N by inventing members that are not in the set and calling them dark. -- Ben.
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| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-06-28 04:32 -0700 |
| Message-ID | <0826afae-1c45-464f-9439-945d5ab66189n@googlegroups.com> |
| In reply to | #603523 |
On Tuesday, June 27, 2023 at 9:43:12 PM UTC-4, Ben Bacarisse wrote:
> Timothy Golden <timba...@gmail.com> writes:
>
> > If he can't name a dark number then it does not exist.
> Have you told him? If so, did he agree?
> > I happen to have a system that allows their naming.
> But can you prove they are in my set N? WM explains the things that
No. I prove that they are beyond the set N.
Infinity is not a bound that can be reached.
As such there are numerous infinities.
Would you care to limit the number of digits in such a value?
Obviously not. Would you care to specify the radix then?
Well, here our human custom is to work in radix ten,
while our machines work in radix two,
but the lowly natural numbers with their successor function at their core are radix one technology.
On matters of infinity I am simply showing that this radix matters.
Standard mathematicians seem to turn their nose up to this detail.
As if radix is arbitrary. It's well proven that this is not the case and we see those side effects. Radix ten values coming out of radix two machines expose this fact.
I'm afraid the sober thing to do is to dismiss all discussion of infinite concern and leave it as untouchable... yet the ellipsis as it has worked its non-halting way into mathematics at the core, such as {1,2,3,...}; and where by the way did Peano trouble over these radix ten instances and their mechanics in his definition of number?; When does working large values start? Is there any distinction to the digits and their relations at a radix point (a decimal point)? It won't be long and these considerations will tempt the subject down a rabbit hole. There are ambiguities afoot.
I don't mean to put a bitter noxious flavor in your mouth here. If anything these weaknesses can be cause to state the subject as lively still, rather than dead and pickled. The only problem really is that you've picked up the pickled version first. To never know the taste of a fresh cucumber is roughly what the status quo would like, and sour pickles for everyone. The same variety; as if there were no value in variation. Is the natural value with a function at the heart of the definition of number really such a refined thing? These functionalists took the grip at some point and shook on everything it seems; even the first form of number. Where would they be without it? What, no structural issues? No compiler error? Oh, great, then let's proceed, humanity, down this dead end path that will always be running the same rabbit loop.
> bother him about infinite sets like N by inventing members that are not
> in the set and calling them dark.
>
> --
> Ben.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-28 15:16 +0100 |
| Message-ID | <87y1k3n04f.fsf@bsb.me.uk> |
| In reply to | #603553 |
Timothy Golden <timbandtech@gmail.com> writes: > On Tuesday, June 27, 2023 at 9:43:12 PM UTC-4, Ben Bacarisse wrote: >> Timothy Golden <timba...@gmail.com> writes: >> >> > If he can't name a dark number then it does not exist. >> Have you told him? If so, did he agree? >> > I happen to have a system that allows their naming. >> But can you prove they are in my set N? WM explains the things that > > No. I prove that they are beyond the set N. So they are not like WM's dark numbers. I thought you claimed to be naming the things WM called dark numbers. The set of things not in N is, well, staggeringly large, so there has to be a very good reason to be interested in them. The rationals and the reals (those not in N) have proved their worth. I wish you luck with your extension to N. -- Ben.
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| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-06-28 07:48 -0700 |
| Message-ID | <647fd866-7612-4041-b812-af306ed90bbdn@googlegroups.com> |
| In reply to | #603557 |
On Wednesday, June 28, 2023 at 10:16:11 AM UTC-4, Ben Bacarisse wrote:
> Timothy Golden <timba...@gmail.com> writes:
>
> > On Tuesday, June 27, 2023 at 9:43:12 PM UTC-4, Ben Bacarisse wrote:
> >> Timothy Golden <timba...@gmail.com> writes:
> >>
> >> > If he can't name a dark number then it does not exist.
> >> Have you told him? If so, did he agree?
> >> > I happen to have a system that allows their naming.
> >> But can you prove they are in my set N? WM explains the things that
> >
> > No. I prove that they are beyond the set N.
> So they are not like WM's dark numbers. I thought you claimed to be
> naming the things WM called dark numbers.
>
> The set of things not in N is, well, staggeringly large, so there has to
> be a very good reason to be interested in them. The rationals and the
> reals (those not in N) have proved their worth. I wish you luck with
> your extension to N.
>
> --
> Ben.
I've already explained it a number of times. Consider the value:
333...33
The ellipsis implies an aleph of digits, and if you opt not to grant this aleph then this entire discussion was already not in your repertoire.
Just as soon as you accepted the aleph of {1,2,3,...}, and it is this same aleph (the radix one form) then it should be clear that the radix ten value that I've given you is obscenely larger than the original aleph. Yet it is also true that this value can represent the increment too:
333...34
Indeed we can even compute not just the sum:
666...67
but the product as well:
111...11222...22
and now we see a next class of infinite value: the quantity of digits in the product is the sum of the digits in the operands. When you thought that two aleph is just the same as one aleph, well, That is clearly not true in the digital form. These forms can sit upon induction and yes, they are limited by the fact that they are getting their largess via repetition and the usage of the ellipsis to imply that. The ellipsis is tied directly to aleph in this way. We could introduce new aleph forms here:
A10 = 999...99
and now that concept of omega as one more:
W10 = 1|000...00
and this 'aleph mark' remedies other potential conflicts, such as whether 10x > x when x=333...33. This value x is far beyond what the naturals will bear. This is due to the digital gain of the radix system. The naturals are bound to the slowest form with their incremental creep.
The only constructive freedom that I've taken is to put a tail on an uncontroversial form. After all the infinite digital sequence has been around:
1/3 = 0.333...
All that I have done is to put a tail on this value:
1/3 = 0.333...33
and of course the radix point deserves scrutiny too, and its correlation with the aleph mark is nearly perfect. Regardless; I did not invent the infinite string of digits; I merely edited it. The conversation does actually broaden out when division is scrutinized, and closure, too. Indeed I got here only after travelling much of that ground, but that said this interpretation as placed here in this one post I find acceptable without that broader loop.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-28 16:43 +0100 |
| Message-ID | <87sfabmw3d.fsf@bsb.me.uk> |
| In reply to | #603563 |
Timothy Golden <timbandtech@gmail.com> writes: > On Wednesday, June 28, 2023 at 10:16:11 AM UTC-4, Ben Bacarisse wrote: >> Timothy Golden <timba...@gmail.com> writes: >> >> > On Tuesday, June 27, 2023 at 9:43:12 PM UTC-4, Ben Bacarisse wrote: >> >> Timothy Golden <timba...@gmail.com> writes: >> >> >> >> > If he can't name a dark number then it does not exist. >> >> Have you told him? If so, did he agree? >> >> > I happen to have a system that allows their naming. >> >> But can you prove they are in my set N? WM explains the things that >> > >> > No. I prove that they are beyond the set N. >> So they are not like WM's dark numbers. I thought you claimed to be >> naming the things WM called dark numbers. >> >> The set of things not in N is, well, staggeringly large, so there has to >> be a very good reason to be interested in them. The rationals and the >> reals (those not in N) have proved their worth. I wish you luck with >> your extension to N. >> > > I've already explained it a number of times. Yes I know and, as I said, I with you luck. I got taken in by your claim to be naming something in N -- specifically what WM calls dark numbers -- not something not in N. -- Ben.
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| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-28 09:49 -0700 |
| Message-ID | <31ddaa7b-5010-430f-b02a-237f6f68a0afn@googlegroups.com> |
| In reply to | #603481 |
Timothy Golden schrieb am Dienstag, 27. Juni 2023 um 17:39:36 UTC+2: > If he can't name a dark number then it does not exist. They can only be named collectively. That's why they are called dark. Regards, WM
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-06-29 09:59 -0400 |
| Message-ID | <5d252867-ec0d-d652-d20a-d4d7917f4876@att.net> |
| In reply to | #603571 |
On 6/28/2023 12:49 PM, WM wrote: > Timothy Golden schrieb am Dienstag, > 27. Juni 2023 um 17:39:36 UTC+2: >> If he can't name a dark number >> then it does not exist. > > They can only be named collectively. > That's why they are called dark. Specifically, that's why you, WM, call them dark. We do not call them dark, except to remark on you calling them dark. Only-able-to-be-named-collectively and not only-able-to-be-named-collectively are not part of how we non-WM describe a natural number or a real number. What we describe we can reason about. By "reason", I mean... We can augment a natural number's description with more claims, using only claims which cannot be first false. This is key: We can _verify_ that our augmenting claims cannot be first false _by looking at the claims_ and nothing more. Do those claims refer to dark numbers? _It doesn't matter_ We've verified their not being first false. What the description is true of the augmenting claims are true of, and _must_ be true of. However, it is incorrect to treat our claims as though they extend beyond what we have described. You could describe something ELSE and augment that OTHER description. You wouldn't be denying OUR claims by doing that, though. It would be like adding up _your_ checkbook and then telling _me_ that _I_ have overdrawn _my_ account. No. It doesn't work like that. It has never, it will never work like that. ---- Only-able-to-be-named-collectively and not only-able-to-be-named-collectively are not part of how we non-WM describe a natural number or a real number. A natural number can be counted to. For natural number k a sequence <0...k> exists such that for each split F||H of <0...k> some i ends its fore segment F and i++ begins its hind segment H F||H = <0...i>||<i++...k> i++ is the successor of i i++ is non-0 non doppelga"nger non-final A real number is a rational number == the ratio of two +-naturals or is between the fore and hind segment of a split of rationals The existence of point-between reals is necessary for us to know that a function which jumps over values is discontinuous somewhere. That is what we mean by natural numbers and real numbers. They are more often described in ways convenient for the work we do with them. "Minimal inductive set" and "complete ordered field", for example. Are there dark numbers among what we mean? In my opinion, that is a badly-asked question, like "Do you still beat your wife?" In my opinion, "dark numbers" is a bit of technobabble which you (WM) deploy in order to deflect from your not-understanding how we know what we _know_ about what we mean by natural numbers and real numbers, the minimal inductive set and the complete ordered field. > Regards, WM
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| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-30 13:04 -0700 |
| Message-ID | <f460761f-3962-4b26-b2fe-6a8450787a73n@googlegroups.com> |
| In reply to | #603623 |
Jim Burns schrieb am Donnerstag, 29. Juni 2023 um 15:59:41 UTC+2: > On 6/28/2023 12:49 PM, WM wrote: > > Timothy Golden schrieb am Dienstag, > > 27. Juni 2023 um 17:39:36 UTC+2: > > >> If he can't name a dark number > >> then it does not exist. > > > > They can only be named collectively. > > That's why they are called dark. > Specifically, > that's why you, WM, call them dark. > We do not call them dark, except > to remark on you calling them dark. > > Only-able-to-be-named-collectively and > not only-able-to-be-named-collectively > are not part of how we non-WM describe > a natural number or a real number. That's why you are so mistaken and erroneous. > > What we describe > we can reason about. > By "reason", I mean... > > We can augment > a natural number's description > with more claims, using only > claims which cannot be first false. Your arguments are irrelevant because they violate three basic principles: Two consecutive actually infinite sets in ℕ are impossible. Increase from 0 to ℵo requires finite intermediate steps 1, 2, 3, ... . Bob does not disappear. > This is key: > We can _verify_ that > our augmenting claims cannot be first false > _by looking at the claims_ > and nothing more. Look at the basic principles. > However, > it is incorrect to treat our claims as though > they extend beyond what we have described. You violate the 3 basic principles. That devalues all your work. > > A natural number can be counted to. Not really. There are 10^80 bits in the universe but there are incompressible numbers with 10^90 bits. You cannot name any of them let alone count to it. > Regards, WM
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-06-30 18:09 -0400 |
| Message-ID | <daab9150-cf8d-201c-5fe5-2595aab31af0@att.net> |
| In reply to | #603710 |
On 6/30/2023 4:04 PM, WM wrote: > Jim Burns schrieb am Donnerstag, > 29. Juni 2023 um 15:59:41 UTC+2: >> Only-able-to-be-named-collectively and >> not only-able-to-be-named-collectively >> are not part of how we non-WM describe >> a natural number or a real number. >> A natural number can be counted to. > > Not really. It's pointless to wrestle you over the name "natural number", when there are so many other things I can call them. I care about _what is named_ Much less so about _the name_ We can reason about infinitely-many things-which-can-be-counted-to, and, yes, a thing-which-can-be-counted-to really can be counted to. Here, I describe what it is to be one of the infinitely-many things-which-can-be-counted-to. For thing-which-can-be-counted-to k a sequence ⟨0…k⟩ exists such that for each split F∥H of ⟨0…k⟩ some i ends its fore segment F and i⁺⁺ begins its hind segment H F∥H = ⟨0…i⟩∥⟨i⁺⁺…k⟩ i⁺⁺ is the successor of i i⁺⁺ is non-0 non-doppelgänger non-final > There are 10^80 bits in the universe > but there are incompressible numbers > with 10^90 bits. > You cannot name any of them > let alone count to it. I claim that I can reason about it, about it and all the other infinitely-many things-which-can-be-counted-to. Whine about "thing-which-can-be-counted-to". Go ahead, knock yourself out. I start from the _description_ and augment the _description_ with further claims which are _visibly_ not first false. I can call them "flying rainbow sparkle ponies", or not not call them anything, and the _important_ part, the _reasoning_ part is utterly unchanged.
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-30 15:18 -0700 |
| Message-ID | <4621ff48-ba4f-4de9-a88b-4ec9b0c5911cn@googlegroups.com> |
| In reply to | #603721 |
On Saturday, July 1, 2023 at 12:10:06 AM UTC+2, Jim Burns wrote: > On 6/30/2023 4:04 PM, WM wrote: > > Jim Burns schrieb am Donnerstag, > > > > > > A natural number can be counted to. > > > > > Not really. Holy shit! Well, yes, but "in principle". When (in the context of set theory), as usual, natural numbers are defined due to von Neumann, then a natural number is the set of all its predecessors - which for each and every natural number is a finite set. Hence each and every narural number (only) has finitely many predecessors. This might justify the claim that "a natural number can be counted to (in principle)".
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-30 15:25 -0700 |
| Message-ID | <80bc8589-4f91-4bfb-8bfb-a9c2c337258fn@googlegroups.com> |
| In reply to | #603722 |
On Saturday, July 1, 2023 at 12:19:02 AM UTC+2, Fritz Feldhase wrote: > On Saturday, July 1, 2023 at 12:10:06 AM UTC+2, Jim Burns wrote: > > On 6/30/2023 4:04 PM, WM wrote: > > > Jim Burns schrieb am Donnerstag, > > > > > > > > A natural number can be counted to. > > > > > > > Not really. > > > > Holy shit! > > Well, yes, but "in principle". > > When (in the context of set theory), as usual, natural numbers are defined due to von Neumann, then a natural number is the set of all its predecessors - which for each and every natural number is a finite set. Hence each and every narural number (only) has finitely many predecessors. > > This might justify the claim that "a natural number can be counted to (in principle)". If each and every "counting step" takes 1 second, then counting to the natural number n takes n seconds - except in Mückenland it seems. If we count with increasing speed, say, 1/2 second to count to 1, 1/2 + 1/4 second(s) to count to 2, 1/2 + 1/4 + 1/8 second(s) to count to 3, etc. then we can count to ANY natural number in under 1 second. (->speed counting)
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| From | FromTheRafters <FTR@nomail.afraid.org> |
|---|---|
| Date | 2023-06-30 18:53 -0400 |
| Message-ID | <u7nmdc$2lnje$1@dont-email.me> |
| In reply to | #603723 |
Fritz Feldhase used his keyboard to write : > On Saturday, July 1, 2023 at 12:19:02 AM UTC+2, Fritz Feldhase wrote: >> On Saturday, July 1, 2023 at 12:10:06 AM UTC+2, Jim Burns wrote: >>> On 6/30/2023 4:04 PM, WM wrote: >>>> Jim Burns schrieb am Donnerstag, >>>>> >>>>> A natural number can be counted to. >>>>> >>>> Not really. >>>> >> Holy shit! >> >> Well, yes, but "in principle". >> >> When (in the context of set theory), as usual, natural numbers are defined >> due to von Neumann, then a natural number is the set of all its predecessors >> - which for each and every natural number is a finite set. Hence each and >> every narural number (only) has finitely many predecessors. >> >> This might justify the claim that "a natural number can be counted to (in >> principle)". > > If each and every "counting step" takes 1 second, then counting to the > natural number n takes n seconds - except in Mückenland it seems. He's using a Thomson's lamp, so sometimes they're dark. > If we count with increasing speed, say, 1/2 second to count to 1, 1/2 + 1/4 > second(s) to count to 2, 1/2 + 1/4 + 1/8 second(s) to count to 3, etc. then > we can count to ANY natural number in under 1 second. (->speed counting) Better call Chuck.
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-30 16:42 -0700 |
| Message-ID | <1e467201-bb0a-4f61-92a9-3d93a46694b1n@googlegroups.com> |
| In reply to | #603725 |
On Saturday, July 1, 2023 at 12:53:40 AM UTC+2, FromTheRafters wrote: > Fritz Feldhase used his keyboard to write : > > > > If we count with increasing speed, say, 1/2 second to count to 1, 1/2 + 1/4 > > second(s) to count to 2, 1/2 + 1/4 + 1/8 second(s) to count to 3, etc. then > > we can count to ANY natural number in under 1 second. (->speed counting) > > > Better call Chuck. Yeah, he's apt to that job.
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| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-07-01 10:19 -0700 |
| Message-ID | <d9f425ef-653e-4d05-af99-7a87a83c3af5n@googlegroups.com> |
| In reply to | #603721 |
Jim Burns schrieb am Samstag, 1. Juli 2023 um 00:10:06 UTC+2: > On 6/30/2023 4:04 PM, WM wrote: > > Jim Burns schrieb am Donnerstag, > > 29. Juni 2023 um 15:59:41 UTC+2: > >> Only-able-to-be-named-collectively and > >> not only-able-to-be-named-collectively > >> are not part of how we non-WM describe > >> a natural number or a real number. > >> A natural number can be counted to. > > > > Not really. > We can reason about infinitely-many > things-which-can-be-counted-to, and, yes, > a thing-which-can-be-counted-to > really can be counted to. You cannot count to 10^10^100. All means of our universe would fail. > > Here, I describe what it is to be > one of the infinitely-many > things-which-can-be-counted-to. Irrelevant. I just describes one of infinitely many that cannot be counted to. > I claim that I can reason about it, > about it and all the other infinitely-many > things-which-can-be-counted-to. Understand why 10^10^100 cannot be counted to. Hint: 10^90 decimals are not available. On earth not even 10^50. If you fail to comprehend this simple point, further discussion is meaningless. Regards, WM
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-07-01 14:06 -0400 |
| Message-ID | <06f3c06b-5a0a-193c-eba2-6ae9ca5c8aa3@att.net> |
| In reply to | #603760 |
On 7/1/2023 1:19 PM, WM wrote: > Jim Burns schrieb am Samstag, > 1. Juli 2023 um 00:10:06 UTC+2: >> On 6/30/2023 4:04 PM, WM wrote: >>> Jim Burns schrieb am Donnerstag, >>> 29. Juni 2023 um 15:59:41 UTC+2: >>>> Only-able-to-be-named-collectively and >>>> not only-able-to-be-named-collectively >>>> are not part of how we non-WM describe >>>> a natural number or a real number. >>>> A natural number can be counted to. >>> >>> Not really. > >> We can reason about infinitely-many >> things-which-can-be-counted-to, and, yes, >> a thing-which-can-be-counted-to >> really can be counted to. > > You cannot count to 10^10^100. For 10^(10^100), a sequence ⟨0…10^(10^100)⟩ exists such that for each split F∥H of ⟨0…10^(10^100)⟩ some i ends its fore segment F and i⁺⁺ begins its hind segment H F∥H = ⟨0…i⟩∥⟨i⁺⁺…10^(10^100)⟩ i⁺⁺ is the successor of i i⁺⁺ is non-0 non-doppelgänger non-final That is what I mean. After you (WM) are done substituting what I don't mean for what I mean, that will still be what I mean. > All means of our universe would fail. In 2023, that is still an open question. Our most recent cosmological observations cannot distinguish the value of the curvature of our cosmos (observable and unobservable) from 0 If that value is negative, our cosmos is infinite. There is, I suppose, a 50% chance that, in some future in which we know more, we will know that it is negative, and we will know that our cosmos is infinite. However that other question resolves, ⟨0…10^(10^100)⟩ exists. >> Here, I describe what it is to be >> one of the infinitely-many >> things-which-can-be-counted-to. > > Irrelevant. No. What I mean is not irrelevant to what I mean. Unfortunately for you, "Quia ego sic dico" does not hold. > I just describes one of infinitely many > that cannot be counted to. And yet, ⟨0…10^(10^100)⟩ exists. >> I claim that I can reason about it, >> about it and all the other infinitely-many >> things-which-can-be-counted-to. > > Understand why 10^10^100 cannot be counted to. > Hint: 10^90 decimals are not available. > On earth not even 10^50. > If you fail to comprehend this simple point, > further discussion is meaningless. And yet, ⟨0…10^(10^100)⟩ exists.
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| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-07-02 07:52 -0700 |
| Message-ID | <4720da7a-1314-4648-9dfe-063217569164n@googlegroups.com> |
| In reply to | #603766 |
Jim Burns schrieb am Samstag, 1. Juli 2023 um 20:06:46 UTC+2: > On 7/1/2023 1:19 PM, WM wrote: > > You cannot count to 10^10^100. > For 10^(10^100), > a sequence ⟨0…10^(10^100)⟩ exists > After you (WM) are done substituting > what I don't mean for > what I mean, No, you are doing so. I said you cannot count to 10^10^100. I did not mention whether a sequence "exists". Not in our universe at least. Simpler for you: You cannot count from 1 to 10^20 using a ten-digit store. > > Understand why 10^10^100 cannot be counted to. > > Hint: 10^90 decimals are not available. > > On earth not even 10^50. > > If you fail to comprehend this simple point, > > further discussion is meaningless. > And yet, ⟨0…10^(10^100)⟩ exists. Many things are claimed to "exist". But religion is not suitable here. I can only talk about provable things. One of them is that you cannot count to 10^10^100. (The others are: Two consecutive actually infinite sets in ℕ are impossible. Increase from 0 to ℵo requires finite intermediate steps 1, 2, 3, ... . Bob does not disappear.) Regards, WM
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| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-07-02 09:48 -0700 |
| Message-ID | <aa308407-79a1-48df-bb45-2617a9d7a692n@googlegroups.com> |
| In reply to | #603809 |
On Sunday, July 2, 2023 at 10:52:22 AM UTC-4, WM wrote:
> Jim Burns schrieb am Samstag, 1. Juli 2023 um 20:06:46 UTC+2:
> > On 7/1/2023 1:19 PM, WM wrote:
>
> > > You cannot count to 10^10^100.
> > For 10^(10^100),
> > a sequence ⟨0…10^(10^100)⟩ exists
> > After you (WM) are done substituting
> > what I don't mean for
> > what I mean,
> No, you are doing so. I said you cannot count to 10^10^100. I did not mention whether a sequence "exists". Not in our universe at least.
>
> Simpler for you: You cannot count from 1 to 10^20 using a ten-digit store.
> > > Understand why 10^10^100 cannot be counted to.
> > > Hint: 10^90 decimals are not available.
> > > On earth not even 10^50.
> > > If you fail to comprehend this simple point,
> > > further discussion is meaningless.
> > And yet, ⟨0…10^(10^100)⟩ exists.
> Many things are claimed to "exist". But religion is not suitable here. I can only talk about provable things. One of them is that you cannot count to 10^10^100. (The others are: Two consecutive actually infinite sets in ℕ are impossible. Increase from 0 to ℵo requires finite intermediate steps 1, 2, 3, ... . Bob does not disappear.)
>
> Regards, WM
There is some trouble as you bend over into 1/n versus n here.
I concur that 10^10^100 is not countable, even by a modern computer. Possibly you've run out of the number of electrons in the universe by this point, thereby obviating the physical possibility as well.
Here again the bump in the road involves mathematics and physics; a false boundary which receives some sort of normalization from each side, but then the two sides are no longer congruent. It's fairly easy to state that 10^10^100 is a valid theoretical natural number. Except for the inclusion of operators denying its pure value, which takes an obnoxious amount of screen space. Then too, just think of the notation in the language of the successor and you'll be troubling badly over the physical limitations.
On the flip side, if we want to study 1/(10^10^100), which is a thing here, clearly we have left the discrete land and attempted a continuum sort of measurement. As strings they can have the same number of digits, a singly unity digit, and a radix point... just reversed:
(10000.) (0.0001) = 1
and off by one... hmmm... perhaps here we've found the mistake of humanity. Perhaps the units digit lays to either side of the radix point, as if to say: "Here is the unity position ... here is the unity position", but that doesn't seem to work well either...
It is only really when we treat the radix point as an addendum to the digital value that it makes sense. Then we can have (1e6)(1e-6)=1.
As to the significance of the digits at such extremes: clearly it is for the left digits to win. The flip side fails to flip here. How did we get those left digits but by building them up from the right? Then we read left to right? Here lays a serious notational issue. Some GI will eventually come along and explain why we shouldn't have flipped things just there; as if our works in words deserve uniqueness to our works in number. Certainly words are numbers too. Certainly, sir. Certifiably so.
The one place it all breaks down is in the radix one terminology, and this arguably is where the natural value is rooted with its successor function defining things. Those mechanics of the radix point are completely gone. Now this ambiguity is a jaw breaker. Stage One numbers don't actually do the things that most people would like them to. The very meaning of unity is altered. Is the radix point nowhere to be found or is it everywhere???
Could it be then that we do have a notational option... to treat a series of numbers as if they are in sum... that we are not even using yet? Doesn't this have physical correspondence? Where did we get those large values from? If it was escapism you were after, I promise you there are better means than mathematics. Peano and his descendants may go down as a pocket of stuffy air after the ground gets leveled.
Two mathematicians; strangers to each other; sat down on a bench in the park at a conference to share their lunch.
"Hey, you got your function in my number.", quipped the one, dipping his celery stick into a jar of peanut butter he was sharing.
"Well, certainly functions without numbers are quite rude.", said the other, dipping his finger directly into the other's jar of peanut butter.
It came out, dripping in a little bit of oil as good peanut butter does, and he choked down the whole gob with a grin and a glare.
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2023-07-02 10:39 -0700 |
| Message-ID | <a7429098-7600-4dca-84fa-a5eb86dddb70n@googlegroups.com> |
| In reply to | #603821 |
On Sunday, July 2, 2023 at 9:48:57 AM UTC-7, Timothy Golden wrote: > On Sunday, July 2, 2023 at 10:52:22 AM UTC-4, WM wrote: > > Jim Burns schrieb am Samstag, 1. Juli 2023 um 20:06:46 UTC+2: > > > On 7/1/2023 1:19 PM, WM wrote: > > > > > > You cannot count to 10^10^100. > > > For 10^(10^100), > > > a sequence ⟨0…10^(10^100)⟩ exists > > > After you (WM) are done substituting > > > what I don't mean for > > > what I mean, > > No, you are doing so. I said you cannot count to 10^10^100. I did not mention whether a sequence "exists". Not in our universe at least. > > > > Simpler for you: You cannot count from 1 to 10^20 using a ten-digit store. > > > > Understand why 10^10^100 cannot be counted to. > > > > Hint: 10^90 decimals are not available. > > > > On earth not even 10^50. > > > > If you fail to comprehend this simple point, > > > > further discussion is meaningless. > > > And yet, ⟨0…10^(10^100)⟩ exists. > > Many things are claimed to "exist". But religion is not suitable here. I can only talk about provable things. One of them is that you cannot count to 10^10^100. (The others are: Two consecutive actually infinite sets in ℕ are impossible. Increase from 0 to ℵo requires finite intermediate steps 1, 2, 3, ... . Bob does not disappear.) > > > > Regards, WM > There is some trouble as you bend over into 1/n versus n here. > I concur that 10^10^100 is not countable, even by a modern computer. Possibly you've run out of the number of electrons in the universe by this point, thereby obviating the physical possibility as well. > > Here again the bump in the road involves mathematics and physics; a false boundary which receives some sort of normalization from each side, but then the two sides are no longer congruent. It's fairly easy to state that 10^10^100 is a valid theoretical natural number. Except for the inclusion of operators denying its pure value, which takes an obnoxious amount of screen space. Then too, just think of the notation in the language of the successor and you'll be troubling badly over the physical limitations. > > On the flip side, if we want to study 1/(10^10^100), which is a thing here, clearly we have left the discrete land and attempted a continuum sort of measurement. As strings they can have the same number of digits, a singly unity digit, and a radix point... just reversed: > (10000.) (0.0001) = 1 > and off by one... hmmm... perhaps here we've found the mistake of humanity. Perhaps the units digit lays to either side of the radix point, as if to say: "Here is the unity position ... here is the unity position", but that doesn't seem to work well either... > > It is only really when we treat the radix point as an addendum to the digital value that it makes sense. Then we can have (1e6)(1e-6)=1. > As to the significance of the digits at such extremes: clearly it is for the left digits to win. The flip side fails to flip here. How did we get those left digits but by building them up from the right? Then we read left to right? Here lays a serious notational issue. Some GI will eventually come along and explain why we shouldn't have flipped things just there; as if our works in words deserve uniqueness to our works in number. Certainly words are numbers too. Certainly, sir. Certifiably so. > > The one place it all breaks down is in the radix one terminology, and this arguably is where the natural value is rooted with its successor function defining things. Those mechanics of the radix point are completely gone. Now this ambiguity is a jaw breaker. Stage One numbers don't actually do the things that most people would like them to. The very meaning of unity is altered. Is the radix point nowhere to be found or is it everywhere??? > > Could it be then that we do have a notational option... to treat a series of numbers as if they are in sum... that we are not even using yet? Doesn't this have physical correspondence? Where did we get those large values from? If it was escapism you were after, I promise you there are better means than mathematics. Peano and his descendants may go down as a pocket of stuffy air after the ground gets leveled. > > Two mathematicians; strangers to each other; sat down on a bench in the park at a conference to share their lunch. > "Hey, you got your function in my number.", quipped the one, dipping his celery stick into a jar of peanut butter he was sharing. > "Well, certainly functions without numbers are quite rude.", said the other, dipping his finger directly into the other's jar of peanut butter. > It came out, dripping in a little bit of oil as good peanut butter does, and he choked down the whole gob with a grin and a glare. Inverse is perhaps the first "axiom". The hyperbola or 1/x is pretty interesting, I've been studying means, and moments and means, about the collections of values by one operation then taking the modular decrement, like the arithmetic and geometric means, about increment (and sum) product (and power) exponent (and tetration) that sort of make for a deconstructive account of arithmetic the usual field of arithmetic, with starting with increment and division instead, what results at elast a model of the same objects. I.e., most people bring an apparatus of number sense that's sort of encumbered, while still it's fruitful and faithful, it's not so much ultimate.
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| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-07-02 13:45 -0700 |
| Message-ID | <e0f3598c-4df5-4997-9207-f29d853dc268n@googlegroups.com> |
| In reply to | #603827 |
On Sunday, July 2, 2023 at 1:39:54 PM UTC-4, Ross Finlayson wrote: > On Sunday, July 2, 2023 at 9:48:57 AM UTC-7, Timothy Golden wrote: > > On Sunday, July 2, 2023 at 10:52:22 AM UTC-4, WM wrote: > > > Jim Burns schrieb am Samstag, 1. Juli 2023 um 20:06:46 UTC+2: > > > > On 7/1/2023 1:19 PM, WM wrote: > > > > > > > > You cannot count to 10^10^100. > > > > For 10^(10^100), > > > > a sequence ⟨0…10^(10^100)⟩ exists > > > > After you (WM) are done substituting > > > > what I don't mean for > > > > what I mean, > > > No, you are doing so. I said you cannot count to 10^10^100. I did not mention whether a sequence "exists". Not in our universe at least. > > > > > > Simpler for you: You cannot count from 1 to 10^20 using a ten-digit store. > > > > > Understand why 10^10^100 cannot be counted to. > > > > > Hint: 10^90 decimals are not available. > > > > > On earth not even 10^50. > > > > > If you fail to comprehend this simple point, > > > > > further discussion is meaningless. > > > > And yet, ⟨0…10^(10^100)⟩ exists. > > > Many things are claimed to "exist". But religion is not suitable here. I can only talk about provable things. One of them is that you cannot count to 10^10^100. (The others are: Two consecutive actually infinite sets in ℕ are impossible. Increase from 0 to ℵo requires finite intermediate steps 1, 2, 3, ... . Bob does not disappear.) > > > > > > Regards, WM > > There is some trouble as you bend over into 1/n versus n here. > > I concur that 10^10^100 is not countable, even by a modern computer. Possibly you've run out of the number of electrons in the universe by this point, thereby obviating the physical possibility as well. > > > > Here again the bump in the road involves mathematics and physics; a false boundary which receives some sort of normalization from each side, but then the two sides are no longer congruent. It's fairly easy to state that 10^10^100 is a valid theoretical natural number. Except for the inclusion of operators denying its pure value, which takes an obnoxious amount of screen space. Then too, just think of the notation in the language of the successor and you'll be troubling badly over the physical limitations. > > > > On the flip side, if we want to study 1/(10^10^100), which is a thing here, clearly we have left the discrete land and attempted a continuum sort of measurement. As strings they can have the same number of digits, a singly unity digit, and a radix point... just reversed: > > (10000.) (0.0001) = 1 > > and off by one... hmmm... perhaps here we've found the mistake of humanity. Perhaps the units digit lays to either side of the radix point, as if to say: "Here is the unity position ... here is the unity position", but that doesn't seem to work well either... > > > > It is only really when we treat the radix point as an addendum to the digital value that it makes sense. Then we can have (1e6)(1e-6)=1. > > As to the significance of the digits at such extremes: clearly it is for the left digits to win. The flip side fails to flip here. How did we get those left digits but by building them up from the right? Then we read left to right? Here lays a serious notational issue. Some GI will eventually come along and explain why we shouldn't have flipped things just there; as if our works in words deserve uniqueness to our works in number. Certainly words are numbers too. Certainly, sir. Certifiably so. > > > > The one place it all breaks down is in the radix one terminology, and this arguably is where the natural value is rooted with its successor function defining things. Those mechanics of the radix point are completely gone. Now this ambiguity is a jaw breaker. Stage One numbers don't actually do the things that most people would like them to. The very meaning of unity is altered. Is the radix point nowhere to be found or is it everywhere??? > > > > Could it be then that we do have a notational option... to treat a series of numbers as if they are in sum... that we are not even using yet? Doesn't this have physical correspondence? Where did we get those large values from? If it was escapism you were after, I promise you there are better means than mathematics. Peano and his descendants may go down as a pocket of stuffy air after the ground gets leveled. > > > > Two mathematicians; strangers to each other; sat down on a bench in the park at a conference to share their lunch. > > "Hey, you got your function in my number.", quipped the one, dipping his celery stick into a jar of peanut butter he was sharing. > > "Well, certainly functions without numbers are quite rude.", said the other, dipping his finger directly into the other's jar of peanut butter. > > It came out, dripping in a little bit of oil as good peanut butter does, and he choked down the whole gob with a grin and a glare. > Inverse is perhaps the first "axiom". > > The hyperbola or 1/x is pretty interesting, I've been studying > means, and moments and means, about the collections of values > by one operation then taking the modular decrement, like the > arithmetic and geometric means, about > > increment (and sum) > product (and power) > exponent (and tetration) > > that sort of make for a deconstructive account of arithmetic > the usual field of arithmetic, with starting with increment > and division instead, what results at elast a model of the same objects. > > I.e., most people bring an apparatus of number sense that's > sort of encumbered, while still it's fruitful and faithful, > it's not so much ultimate. Very nice. In doing so you do achieve halting status. As well, gravity in the classical form isn't far away as: F = ( m1 / r1 )( m2 / r2) and it happens that r1 and r2 are the same thing in ordinary mechanics. In that the sum is physically inherent, then it would be truthful that the decomposition involves its inverse. In that this classical gravitation above has plucked two objects out of reality and allows us to fictitiously resolve the problem... we are fortunate to have one sun in the solar system to get things started. I accept that there is cause for this metric I will mention, and it can be had by any tape measure, but a slight modification is needed. First cut off the first inch. This is the division by zero problem gone. In effect do not allow the 1/r problem by denying the first inch; simply cut it off so that: y = 1/(r1+1) becomes the proper transform, where 'r' is the ordinary tape measure, and y is the new one, which reads the same except you snip off the first inch and put a '1/' ahead of every mark. Now gravity has a full product relationship: F= (m1y1)(m2y2) but the 'metric' is not the usual continuum type. Why we use large numbers for things distant to us, which are less important, can be a rough beginning on this interpretation. As to that which is adjacent: can it really be said to have zero distance? I suppose it is more likely that I will be affected by the leaf on a tree at ten meters than a galaxy at 10^10 meters, right? Maybe I'm off a little bit there, but you get the point. From the physical sensibilities, closure is not actually necessary, especially under product. With three golf balls in my left hand and two in my right their product may be six, yet I will still have only five golf balls. This awareness of closure is where your decremental consideration shines some. defining operators as functions does less for the situation than some think. Being off by say a Planck unit that even derives the unital distance would be a wonderful result that could give mathematicians a breather. That doesn't have to put us on a discrete lattice though. In effect, if this were adopted then what should have been the real number will not overlap the naturals so readily. The field requirements have an exception and that should be a problem instead of a solution.
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