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Re: how

From Richard Damon <richard@damon-family.org>
Newsgroups sci.math
Subject Re: how
Date 2024-04-24 19:13 -0400
Organization i2pn2 (i2pn.org)
Message-ID <v0c3nd$2538n$6@i2pn2.org> (permalink)
References (6 earlier) <MhMKLiWFUW2BGqeHumLSqLhBo1I@jntp> <v06q93$1uk1v$3@i2pn2.org> <Fr-J6IVJwWMeVOUV5nUftUgP93w@jntp> <v09p60$222fd$4@i2pn2.org> <4dXo8hjS-AzHfYNb1eEKYA7PWS4@jntp>

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On 4/24/24 1:16 PM, WM wrote:
> Le 24/04/2024 à 04:01, Richard Damon a écrit :
>> 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.
> 
>> Why?
> 
> Continuity.

Who says we have that sort of "Continuity"?

Infinite numbers don't behave the same as what we expect out of finite 
numbers.


>>
>> [0, ω]*2 = { [0, w), ω } *2 = {[0, w), ω*2} since the Natural numbers 
>> (what [0, ω) represents) are closed under multiplication.
> 
> Impossible if (0, ω) is completely filled. Every 2n is larger than n.

Right, 2n is greater than n but still finite and < ω. That is the nature 
of unbounded sets, and blows up your finite logic.

>>
>> 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, ...
> 
> Here are always gaps of one unit. Between ω and ω2 is an infinite 
> emptiness.

Right, because they are a different type of Ordinals. Between ω and ω+1 
is one step, between 0, ω, 2ω, 3ω, ... is a first order infinite step.

> 
> Crippled ugly mathematics.

Just beyound your ability to comprehend. You just can't appreciate the 
beauty of infinity because it blows out your mind that is just too small.

> 
> Regards, WM
> 

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  Re: how Richard Damon <richard@damon-family.org> - 2024-04-09 19:06 -0400
    Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-10 18:03 +0000
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                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-26 17:02 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-26 09:26 -0400
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-26 17:33 +0200
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-26 13:14 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-23 21:50 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 17:06 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-24 19:34 +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 20:17 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-25 22:04 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-05-03 20:22 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 18:55 -0400
                Re: how Moebius <moebius@example.invalid> - 2024-04-21 18:07 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 15:10 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 18:04 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 18:58 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 18:35 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-23 20:47 +0200
                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 Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-15 12:56 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-15 16:57 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-16 02:03 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-16 12:50 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-18 09:09 -0700
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-05-18 14:16 -0400
                Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-18 13:11 -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 19:25 -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

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