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Re: Contradiction of bijections as a measure for infinite sets

From Jim Burns <james.g.burns@att.net>
Newsgroups sci.math
Subject Re: Contradiction of bijections as a measure for infinite sets
Date 2024-04-07 17:47 -0400
Organization A noiseless patient Spider
Message-ID <a91c158a-b4eb-405f-bf7d-7704d7fb171b@att.net> (permalink)
References (6 earlier) <6VFp9Pr9I394XSyRAi0w-GMz2GY@jntp> <373b543f-be44-4441-b9d3-9fdb44287e95@att.net> <ymJoogUCploI4Stcei3A4L4PLPg@jntp> <fa45fae3-33bd-495d-8415-07804b36f6f8@att.net> <780i3eKdKZ5P_9FaZ1WI-mHhUTs@jntp>

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On 4/6/2024 3:49 PM, WM wrote:
> Le 06/04/2024 à 17:49, Jim Burns a écrit :
>> On 4/6/2024 9:44 AM, WM wrote:

>>> But we can use the ordinal axis
>>> as Cantor has described it
>>> 0, 1, 2, 3, ...,
>>> ω, ω + 1, ..., ω + k, ...,
>>> ω + ω (= ω2), ω2 + 1, ..
>>> and multiply 0, 1, 2, 3, ..., ω, by 2.
>>
>> Two times anything on the first row
>> is something on the first row.
>
> That is contradicted by

...your anti.arithmetism.

tl;dr
The successor operation is closed in
the natural numbers.
Natural.number.addition is closed in
the natural numbers.
Natural.number.multiplication is closed in
the natural numbers.

Those claims are theorems.
In order to be theorems,
it is important to know the meaning of
successor, natural number, addition and multiplication.

If you want to see the proofs, ask.

Consider the successor.operation ⁺¹ which is
non.0, 1.to.1, and closed in the successor.havers.
i⁺¹≠0 ∧ ¬∃h≠i:h⁺¹=i⁺¹ ∧ ∃k=i⁺¹⁺¹ ∧ 1=0⁺¹

For some successor.havers k
a set ⟦0,k⦆ exists such that
predecessor k⁻¹ of k  and
predecessor i⁻¹ of each i≠0 in ⟦0,k⦆  and
0 are in ⟦0,k⦆
∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧

The natural numbers ℕ are
0 and successor.havers with ⟦0,k⦆ like that
k ∈ ℕ  ⟺
k=0 ∨ ∃⟦0,k⦆: ∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧

That successor operation ⁺¹ is closed in ℕ
If
∃⟦0,k⦆: ∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧
then
∃⟦0,k⁺¹⦆: ∀i ∈ ⟦0,k⁺¹⦆: i⁺¹ ∈ ⦅0,k⁺¹⟧
Thus,
if k ∈ ℕ
then k⁺¹ ∈ ℕ

Addition in ℕ is defined so that
k+m=n  ⟺
a sequence fₖ₊ₘ₌ₙ: ⟦0,m⟧ ⟶ 𝔸 exists of addition.facts
starting with ⟨k+0=k⟩, ending with ⟨k+m=n⟩
and ⟨k+i=j⟩ ⇔ ⟨k+i⁺¹=j⁺¹⟩
∀k,m,n ∈ ℕ:
k+m=n  ⟺
∃fₖ₊ₘ₌ₙ: ⟦0,m⟧ ⟶ 𝔸:
fₖ₊ₘ₌ₙ(0)=⟨k+0=k⟩ ∧ fₖ₊ₘ₌ₙ(m)=⟨k+m=n⟩ ∧
∀i ∈ ⟦0,m⦆:
fₖ₊ₘ₌ₙ(i)=⟨k+i=j⟩ ⇔ fₖ₊ₘ₌ₙ(i⁺¹)=⟨k+i⁺¹=j⁺¹⟩

Addition in ℕ is closed in ℕ
If
∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧  and
∀i ∈ ⟦0,m⦆: i⁺¹ ∈ ⦅0,m⟧
then
∀i ∈ ⟦0,k+m⦆: i⁺¹ ∈ ⦅0,k+m⟧
Thus,
if k,m ∈ ℕ
then k+m ∈ ℕ

Multiplication in ℕ is defined so that
k⋅m=n  ⟺
a sequence fₖ.ₘ₌ₙ: ⟦0,m⟧ ⟶ 𝕄 exists of multiplication.facts
starting with ⟨k⋅0=0⟩, ending with ⟨k⋅m=n⟩
and ⟨k⋅i=j⟩ ⇔ ⟨k⋅i⁺¹=j+k⟩
∀k,m,n ∈ ℕ:
k⋅m=n  ⟺
∃fₖ.ₘ₌ₙ: ⟦0,m⟧ ⟶ 𝕄:
fₖ.ₘ₌ₙ(0)=⟨k⋅0=0⟩ ∧ fₖ.ₘ₌ₙ(m)=⟨k⋅m=n⟩ ∧
∀i ∈ ⟦0,m⦆:
fₖ.ₘ₌ₙ(i)=⟨k+i=j⟩ ⇔ fₖ.ₘ₌ₙ(i⁺¹)=⟨k+i⁺¹=j+k⟩

Multiplication in ℕ is closed in ℕ
If
∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧  and
∀i ∈ ⟦0,m⦆: i⁺¹ ∈ ⦅0,m⟧
then
∀i ∈ ⟦0,k⋅m⦆: i⁺¹ ∈ ⦅0,k⋅m⟧
Thus,
if k,m ∈ ℕ
then k⋅m ∈ ℕ

> That is contradicted by this argument:
> Two times all numbers of 1, 2, 3, .., ω
> will double the distance between ℕ and ω
> to that between 2ℕ and 2ω.

No, it won't.

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V WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:00 +0000
  Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 13:11 -0700
    Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:13 +0000
      Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 13:16 -0700
        Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:20 +0000
          Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 14:33 -0700
            Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:23 +0000
              Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-25 20:40 -0700
                Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:11 +0000
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 12:56 -0700
                Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:50 +0000
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:49 -0700
                Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 19:53 +0000
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 13:31 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 13:34 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:00 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:19 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:29 -0700
          Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 14:37 -0700
  Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:11 +0000
    Re: Contradiction of bijections as a measure for infinite sets Dieter Heidorn <d.heidorn@t-online.de> - 2024-03-24 22:02 +0100
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:10 +0000
        Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-25 07:25 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 21:45 +0000
        Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-25 15:38 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 22:01 +0000
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 22:11 +0000
            Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-25 20:04 -0400
              Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-25 21:43 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-26 11:40 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:38 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-27 14:54 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 20:07 +0000
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 13:33 -0700
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 09:29 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:01 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-30 13:47 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-31 12:15 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-31 14:18 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:37 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-01 13:30 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-01 19:03 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-02 07:36 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 13:51 -0400
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-02 22:52 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 17:40 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-02 15:06 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 19:25 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-02 20:52 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-03 09:13 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-03 19:13 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-04 15:01 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-04 20:28 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-05 14:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-05 19:37 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-06 09:31 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-06 08:42 -0700
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-03 01:14 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-03 13:32 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-03 11:59 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-03 19:43 -0700
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-03 20:06 -0700
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-05 08:48 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-04 09:33 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-04 08:19 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-04 13:07 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-04 09:22 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-05 08:56 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-05 07:32 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-05 19:30 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-04 15:40 +0200
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-05 08:57 -0400
                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
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-07 13:23 +0000
                how Richard Damon <richard@damon-family.org> - 2024-04-07 13:56 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-08 13:44 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-08 19:22 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-09 12:16 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 16:00 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 16:02 -0700
                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
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-10 19:04 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-11 12:03 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-11 18:32 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 13:40 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 09:58 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:37 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 10:56 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-10 20:14 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-10 18:47 -0400
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-10 19:05 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-11 12:07 +0000
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-11 13:36 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 13:18 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 15:56 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:32 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 16:38 +0200
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 16:40 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:44 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 10:57 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 15:22 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 17:43 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 11:47 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 16:35 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 12:58 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-13 12:23 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-13 08:59 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-14 19:05 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-14 15:19 -0400
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-14 18:25 -0400
                Re: how Hayward Böhm Geissler <red@yiwra.de> - 2024-04-13 15:41 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:14 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 17:00 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 15:26 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 17:51 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 16:40 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 18:44 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:16 -0700
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-12 18:22 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-13 12:12 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:04 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:03 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 23:51 +0200
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-12 14:57 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-13 12:35 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-13 09:05 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-14 19:07 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-14 15:23 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-15 11:47 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-15 14:54 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 14:24 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-15 18:38 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 14:59 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-16 19:27 -0400
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-17 01:47 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-16 22:51 -0700
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-17 02:02 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-17 11:44 -0700
                Re: how is arithmetic composed of separately increment and division Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-17 21:02 -0700
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-17 18:49 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-17 11:54 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-17 18:59 -0400
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 01:10 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-18 14:59 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-18 11:34 -0400
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-18 18:42 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-19 15:37 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-19 13:04 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-19 22:57 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-19 21:31 -0700
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 16:26 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-20 13:42 -0400
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-20 20:01 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 18:34 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-20 18:44 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 15:01 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 18:02 +0200
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-22 14:02 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 18:06 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-23 14:57 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-23 19:13 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-23 15:56 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 16:59 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-23 14:23 -0700
                Re: how Moebius <moebius@example.invalid> - 2024-04-23 23:44 +0200
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-23 20:03 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-24 17:05 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-24 19:30 +0200
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-24 14:50 -0400
                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> - 2024-04-22 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 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 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 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> - 2024-04-24 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 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 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 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 Moebius <moebius@example.invalid> - 2024-04-22 20:48 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-22 15:36 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-22 21:40 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-22 21:44 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-23 01:01 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-22 20:52 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-22 17:03 -0400
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-22 19:23 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-23 01:28 +0200
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-22 20:12 -0400
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how Moebius <moebius@example.invalid> - 2024-04-23 02:21 +0200
                Re: because g?(g?¹(x)) = g(y) [1/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-22 21:03 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 19:07 -0400
                because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-18 18:09 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-19 15:15 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-19 10:27 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Jim Burns <james.g.burns@att.net> - 2024-04-19 18:24 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 16:31 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 12:40 -0400
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 16:57 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 13:15 -0400
                Re: because g?(g?¹(x)) = g(y) [2/2] Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-20 13:46 -0400
                Re: because g?(g?¹(x)) = g(y) [2/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 18:35 +0000
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Moebius <moebius@example.invalid> - 2024-04-21 18:22 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 15:14 +0000
                Re: how can a person be so dumb? Moebius <moebius@example.invalid> - 2024-04-22 17:51 +0200
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-19 09:36 -0700
                Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-20 12:52 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-15 23:35 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-16 14:38 +0000
                Re: how Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-14 08:40 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-11 21:16 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 13:45 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 10:02 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:40 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 11:01 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:19 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 22:31 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:46 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-10 18:16 -0700
                Re: how Phil Carmody <pc+usenet@asdf.org> - 2024-04-18 02:12 +0300
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-18 15:08 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-18 17:20 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-18 18:40 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-19 15:39 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-19 19:38 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 16:42 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 13:17 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-20 18:40 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-20 14:49 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 14:25 +0000
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 16:37 +0200
                Re: how Moebius <moebius@example.invalid> - 2024-04-22 16:40 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 19:12 -0400
                Re: how Moebius <moebius@example.invalid> - 2024-04-21 18:32 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-22 15:19 +0000
                Re: how (holy shit!) Moebius <moebius@example.invalid> - 2024-04-22 17:59 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-22 16:21 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-22 19:38 -0400
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-03 19:48 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-04 09:43 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-04 13:03 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-05 09:06 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-05 15:03 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:44 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-06 13:49 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 19:49 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-07 17:47 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-08 13:55 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-08 21:54 -0400
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 04:48 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-09 23:46 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-09 12:22 +0000
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-09 14:47 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 15:03 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-09 17:15 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 18:44 +0200
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 15:49 -0700
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 15:04 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-09 16:27 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-10 17:57 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-10 16:13 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-10 17:39 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-11 11:16 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-09 18:42 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 15:59 -0700
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-10 05:37 +0200
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-10 11:47 -0700
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 15:47 -0700
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-13 23:15 -0700
                Re: Contradiction of bijections as a measure for infinite sets Dieter Heidorn <d.heidorn@t-online.de> - 2024-04-14 14:35 +0200
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-31 13:20 -0700
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-27 20:52 -0400
              Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:24 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-26 13:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:46 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-27 15:10 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:57 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-27 18:50 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-26 21:19 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:57 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-27 20:57 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 20:00 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 09:31 -0400
    Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-24 17:09 -0400
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:15 +0000
        Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-25 07:29 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 21:49 +0000
    Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-24 17:10 -0400
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:20 +0000
        Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-25 14:31 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 21:53 +0000
            Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-25 18:49 -0400
              Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:18 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-26 09:39 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:47 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-26 14:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets Phil Carmody <pc+usenet@asdf.org> - 2024-03-26 23:12 +0200
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-26 17:40 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 19:43 -0700
                Re: Contradiction of bijections as a measure for infinite sets Phil Carmody <pc+usenet@asdf.org> - 2024-03-27 13:35 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:48 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-27 11:23 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 21:50 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-27 19:37 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 19:55 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-28 18:11 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 13:05 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:05 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-30 13:48 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-27 20:59 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 19:57 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 13:07 -0400
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-28 17:25 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 21:40 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-28 18:30 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 17:54 -0700
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 18:00 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-29 05:46 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:53 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-29 15:13 +0100
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:52 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-30 00:29 +0100
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 16:31 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-30 09:56 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:17 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-30 15:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-31 12:20 +0000
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 15:19 +0200
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-31 08:10 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 17:31 +0200
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-31 14:10 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 17:38 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-31 13:38 -0400
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-31 15:37 -0400
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-31 15:43 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:34 +0000
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:11 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:14 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-01 14:34 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-02 07:32 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 11:35 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-03 13:29 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-03 17:07 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:09 +0000
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-31 19:14 +0200
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-31 13:22 -0700
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:30 +0000
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:26 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 22:41 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-29 15:09 +0100
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-29 17:31 +0100
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-31 19:17 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 19:37 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 19:44 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:24 +0000
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-30 17:37 +0100
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-31 03:57 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-05 22:07 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:47 +0000
    Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-30 23:53 +0100
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:04 +0000
        Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:37 +0200
          Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-01 20:47 +0200

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