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Groups > sci.math > #627161

Re: how

From Richard Damon <richard@damon-family.org>
Newsgroups sci.math
Subject Re: how
Date 2024-04-23 22:01 -0400
Organization i2pn2 (i2pn.org)
Message-ID <v09p60$222fd$4@i2pn2.org> (permalink)
References (6 earlier) <x_NkVA7tC4PbuDHgWd_lI0r3UuA@jntp> <v012ji$1m94d$4@i2pn2.org> <MhMKLiWFUW2BGqeHumLSqLhBo1I@jntp> <v06q93$1uk1v$3@i2pn2.org> <Fr-J6IVJwWMeVOUV5nUftUgP93w@jntp>

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On 4/23/24 3:34 PM, WM wrote:
> Le 23/04/2024 à 01:01, Richard Damon a écrit :
>> On 4/22/24 10:15 AM, WM wrote:
> 
>>> The results cannot be compressed to the interval (0, ω) of the set { 
>>> 1, 2, 3, ...}. This shows that new numbers are generated by 
>>> multiplication.
>>>
>> Of course they can be compressed into the interval (0, ω), as every 
>> finite number n < ω, when doubled results in a finite number 2n which 
>> is also < ω.
> 
> Try to map the closed interval [0, ω]*2 = [0, ω*2].
> If [0, ω) --> [0, ω) and ω*2 --> ω*2, then ω*2 is the only image point 
> in (ω, ω*2]. Infinitely many points remain empty. Crippled mathematics. 
> Ugly. Inacceptable.
> 
> Regards, WM
> 
> 
> 

Why?

[0, ω]*2 = { [0, w), ω } *2 = {[0, w), ω*2} since the Natural numbers 
(what [0, ω) represents) are closed under multiplication.

The fact that a mixed set of two different classes of ordinals ends up 
with two different classes of ordinals isn't surprizing.

The fact that there are "gaps" in the result isn't surprising, as we see 
the same gaps in the finite part of the set:

0, 1, 2, 3 ... *2 => 0, 2, 4, 6, ...

so the fact that 1 disappeared into a gap in the result says the gap 
between the finites and ω*2 is reasonable.

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Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:26 +0000
  Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-06 09:40 -0400
    Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:55 +0000
      Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-06 09:58 -0400
        Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 19:40 +0000
          Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-06 16:03 -0400
            Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-07 08:32 +0000
              Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-07 07:16 -0400
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                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 19:06 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-23 21:30 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-23 14:24 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-23 14:27 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-23 23:27 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-03 20:30 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-23 21:52 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 17:09 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-24 20:22 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-24 19:13 -0400
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-19 17:44 -0400
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-19 19:32 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 16:39 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 13:05 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 18:31 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 14:47 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 14:15 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 16:31 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 19:01 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 18:42 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-23 20:54 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-23 21:57 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 19:34 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-23 21:45 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 19:51 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-23 22:03 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 17:01 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-24 19:40 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-25 19:40 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-25 21:47 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-25 20:27 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-25 22:40 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-25 22:07 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-25 19:37 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-23 22:03 -0400
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-24 06:49 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 17:10 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-24 14:08 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-25 19:51 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-25 19:03 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-26 14:32 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-26 13:53 -0400
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-25 22:08 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-26 17:06 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-26 15:10 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-27 14:54 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-27 13:38 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-30 13:00 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-30 18:50 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-03 13:23 +0000
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 17:12 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-23 22:01 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 17:16 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-24 19:49 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-24 13:07 -0700
                Re: how Moebius <moebius@example.invalid> - 2024-04-24 22:34 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-24 13:36 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-24 13:38 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-24 13:44 -0700
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-24 19:49 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-24 17:08 -0700
                Re: how Moebius <moebius@example.invalid> - 2024-04-25 02:30 +0200
                Re: how Moebius <moebius@example.invalid> - 2024-04-25 02:17 +0200
                Re: how Moebius <moebius@example.invalid> - 2024-04-25 02:40 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-24 17:48 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-24 17:49 -0700
                Re: how Moebius <moebius@example.invalid> - 2024-04-25 03:16 +0200
                Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-24 19:55 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-25 12:10 -0700
                Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-25 13:35 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-26 12:53 -0700
                Re: how Moebius <moebius@example.invalid> - 2024-04-25 03:10 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-25 12:23 -0700
                Re: how Moebius <moebius@example.invalid> - 2024-04-26 00:12 +0200
                Re: how Moebius <moebius@example.invalid> - 2024-04-26 00:14 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-25 19:44 -0700
                Re: how Moebius <franz.fritsche@yahoo.de> - 2024-04-30 01:12 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-25 20:06 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-26 13:01 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-26 23:48 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-26 18:01 -0400
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-27 00:10 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-24 19:13 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-25 20:20 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-25 15:01 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-25 15:07 -0700
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-13 15:16 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-14 19:12 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-14 22:17 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-15 11:53 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-15 15:00 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-15 12:22 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-15 22:13 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-15 15:45 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-16 01:44 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-15 18:47 -0700
                Re: how Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2024-04-16 01:35 +0100
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 15:05 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-16 18:14 +0200
                Re: how Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2024-04-16 17:38 +0100
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 18:36 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-16 21:48 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-17 18:37 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-17 21:38 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-17 20:30 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-17 22:55 +0200
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 01:05 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-17 19:26 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-18 15:05 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 17:19 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-18 18:35 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-19 15:20 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-19 13:06 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-19 22:58 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-28 16:54 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-19 19:36 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-19 21:33 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 09:10 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 16:40 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 13:09 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 18:38 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 14:48 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 14:20 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 19:04 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 19:04 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 18:45 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-23 22:27 -0400
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 19:27 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 17:53 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 20:20 +0200
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 20:34 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 18:15 +0000
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 18:02 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-22 18:11 -0700
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 18:52 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-20 07:34 -0400
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 09:07 -0400
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 19:17 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-16 19:29 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-16 20:17 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-16 20:19 -0700
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-17 18:52 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-17 19:30 -0400
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 01:41 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-18 15:15 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 17:42 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-18 15:13 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 17:29 +0200
                Re: how Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2024-04-18 17:59 +0100
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 19:30 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 14:27 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-16 18:09 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 18:40 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-16 21:53 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-17 18:39 +0000
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-14 16:39 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-14 20:38 -0700
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-15 11:59 +0000
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-15 17:06 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 14:33 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-16 18:11 +0200
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-17 18:50 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-18 14:54 +0000
                because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-18 18:09 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-19 15:05 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-19 15:16 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 16:23 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-21 14:08 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 15:35 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-22 18:08 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 17:45 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-22 20:17 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 19:07 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-22 13:32 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 17:56 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-22 23:51 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 18:57 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-23 15:55 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 16:57 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-24 20:01 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-25 19:43 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-24 15:42 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-25 20:03 +0000
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-25 19:09 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-25 19:11 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-26 01:57 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-26 14:37 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-26 14:53 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-26 21:27 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-01 18:46 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Tom Bola <Tom@bolamail.etc> - 2024-05-02 01:32 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-02 14:00 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Tom Bola <Tom@bolamail.etc> - 2024-05-02 20:49 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-03 05:07 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Tom Bola <Tom@bolamail.etc> - 2024-05-03 15:07 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-03 13:57 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Tom Bola <Tom@bolamail.etc> - 2024-05-03 16:09 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-03 14:12 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Tom Bola <Tom@bolamail.etc> - 2024-05-03 16:15 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-03 14:49 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-03 15:32 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-03 20:31 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-03 14:50 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-03 19:01 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-05 13:59 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-05 11:30 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-05 18:02 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-06 12:36 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-06 16:15 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-07 13:22 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-08 14:40 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-08 13:20 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-08 17:14 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-09 12:56 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-09 18:55 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-09 18:45 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-10 06:59 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-10 13:12 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-10 18:26 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-10 17:17 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-11 04:18 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 06:38 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-11 10:40 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 08:47 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-11 15:24 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 14:05 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 14:44 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 16:11 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-11 19:47 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 18:17 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 18:44 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-12 11:08 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-12 13:46 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-12 11:21 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-12 12:34 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-13 00:11 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-13 13:22 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-13 13:43 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-14 13:15 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-15 10:10 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-11 19:25 -0400
                Re: universal quantification, because g?(g?¹(x)) = g(y) [1/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-11 07:02 -0400
                Re: universal quantification, because g?(g?¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-11 06:44 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-06 18:59 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-06 16:16 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-06 20:28 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-06 18:11 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-08 19:55 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-08 17:55 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-09 02:27 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-09 02:54 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-09 03:11 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-10 12:24 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-08 21:14 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-09 02:35 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-09 02:42 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-08 21:14 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-10 12:31 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-10 12:18 +0000
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-10 10:59 -0400
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-13 20:21 +0000
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-13 18:47 -0400
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-14 11:10 +0000
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-05-14 10:15 -0400
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-15 13:13 +0000
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-13 16:32 -0700
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-14 11:15 +0000
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-14 16:26 +0200
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-14 17:24 +0200
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-15 13:18 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-10 14:56 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-10 21:34 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-10 19:44 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-11 05:00 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-11 05:32 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-11 14:49 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-11 17:01 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <invalid@example.invalid> - 2024-05-11 05:26 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-13 20:31 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-05-13 20:27 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-13 16:33 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-10 13:31 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-10 13:37 -0700

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