Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

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Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.math
Date : 05. Dec 2024, 23:20:10
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <ae606e53-0ded-4101-9685-fa33c9a35cb9@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
User-Agent : Mozilla Thunderbird
On 12/5/2024 2:30 PM, WM wrote:
On 05.12.2024 18:12, Jim Burns wrote:
On 12/5/2024 4:00 AM, WM wrote:
On 04.12.2024 21:36, Jim Burns wrote:

No intersection of
more.than.finitely.many end.segments
of the finite.cardinals
holds a finite.cardinal,  or
is non.empty.
>
Small wonder.
More than finitely many endsegments
require
infinitely many indices, i.e., all indices.
No natnumbers are remaining in the contents.
>
⎛ That's the intersection.
>
And it is the empty endsegment.
Depending upon how 'end.segment' is defined,
{} either is or isn't an end.segment.
Consider the options.
⎛ With {} as an end.segment,
⎜ there are more.than.finite.many end.segments,
⎜ too many for any finite.cardinal to be
⎜ in common with all end segments.
⎜ And therefore,
⎜ the intersection of all holds no finite cardinal.

⎜ With {} NOT as an end.segment,
⎜ there STILL are more.than.finite.many end.segments,
⎜ too many for any finite.cardinal to be
⎜ in common with all end segments.
⎜ And therefore,
⎝ the intersection of all STILL holds no finite cardinal.
The intersection of all non.empty.end.segments
of the finite.cardinals,
which are each infinite non.empty.end.segments,
is empty.
Because,
⎛ for each finite.cardinal,
⎜ there are fewer finite.cardinals before it
⎝ than there are finite.cardinals after it.
Not because
( an end.segment is empty.

Date Sujet#  Auteur
27 Nov 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)388WM
27 Nov 24 +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2joes
27 Nov 24 i`- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
28 Nov 24 `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)385Jim Burns
28 Nov 24  +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)383WM
28 Nov 24  i+* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)375joes
28 Nov 24  ii`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)374WM
28 Nov 24  ii +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)4joes
28 Nov 24  ii i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3WM
28 Nov 24  ii i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2joes
28 Nov 24  ii i  `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
28 Nov 24  ii `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)369FromTheRafters
28 Nov 24  ii  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)368WM
29 Nov 24  ii   +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2joes
29 Nov 24  ii   i`- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
29 Nov 24  ii   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)365FromTheRafters
29 Nov 24  ii    +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)363WM
29 Nov 24  ii    i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)362FromTheRafters
29 Nov 24  ii    i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)361WM
29 Nov 24  ii    i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)360FromTheRafters
30 Nov 24  ii    i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)359WM
30 Nov 24  ii    i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)358FromTheRafters
30 Nov 24  ii    i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)357WM
30 Nov 24  ii    i      +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)10FromTheRafters
30 Nov 24  ii    i      i+* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)7WM
30 Nov 24  ii    i      ii`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)6joes
30 Nov 24  ii    i      ii `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)5WM
30 Nov 24  ii    i      ii  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)4joes
30 Nov 24  ii    i      ii   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3WM
1 Dec 24  ii    i      ii    `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2joes
1 Dec 24  ii    i      ii     `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
30 Nov 24  ii    i      i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, infinite-middle)2Ross Finlayson
2 Dec 24  ii    i      i `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, infinite-middle)1Chris M. Thomasson
2 Dec 24  ii    i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)346Chris M. Thomasson
2 Dec 24  ii    i       +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)90Moebius
3 Dec 24  ii    i       i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)89Chris M. Thomasson
3 Dec 24  ii    i       i +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)84Moebius
3 Dec 24  ii    i       i i+- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Chris M. Thomasson
3 Dec 24  ii    i       i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)82Chris M. Thomasson
3 Dec 24  ii    i       i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)81Moebius
3 Dec 24  ii    i       i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)80Chris M. Thomasson
3 Dec 24  ii    i       i i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)79Chris M. Thomasson
3 Dec 24  ii    i       i i    +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)17Moebius
3 Dec 24  ii    i       i i    i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)16Chris M. Thomasson
3 Dec 24  ii    i       i i    i +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3Chris M. Thomasson
3 Dec 24  ii    i       i i    i i+- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Chris M. Thomasson
3 Dec 24  ii    i       i i    i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Moebius
3 Dec 24  ii    i       i i    i +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2Moebius
3 Dec 24  ii    i       i i    i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
3 Dec 24  ii    i       i i    i +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)9Chris M. Thomasson
3 Dec 24  ii    i       i i    i i+* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)7Chris M. Thomasson
3 Dec 24  ii    i       i i    i ii`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)6Chris M. Thomasson
3 Dec 24  ii    i       i i    i ii +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)4Moebius
3 Dec 24  ii    i       i i    i ii i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3Moebius
3 Dec 24  ii    i       i i    i ii i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2Chris M. Thomasson
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3 Dec 24  ii    i       i i    i ii `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Chris M. Thomasson
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3 Dec 24  ii    i       i i     +- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
3 Dec 24  ii    i       i i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)59Chris M. Thomasson
4 Dec 24  ii    i       i i      +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)55Moebius
4 Dec 24  ii    i       i i      i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)54Moebius
4 Dec 24  ii    i       i i      i +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)52Chris M. Thomasson
4 Dec 24  ii    i       i i      i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)51Moebius
4 Dec 24  ii    i       i i      i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)50Moebius
4 Dec 24  ii    i       i i      i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)49FromTheRafters
4 Dec 24  ii    i       i i      i i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)48Ben Bacarisse
4 Dec 24  ii    i       i i      i i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)47Moebius
4 Dec 24  ii    i       i i      i i     +- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1FromTheRafters
4 Dec 24  ii    i       i i      i i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)45Ben Bacarisse
4 Dec 24  ii    i       i i      i i      +- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1FromTheRafters
4 Dec 24  ii    i       i i      i i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)43Chris M. Thomasson
4 Dec 24  ii    i       i i      i i       +- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Ben Bacarisse
5 Dec 24  ii    i       i i      i i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)41WM
5 Dec 24  ii    i       i i      i i        +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)19joes
5 Dec 24  ii    i       i i      i i        i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)18WM
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5 Dec 24  ii    i       i i      i i        i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)7WM
6 Dec 24  ii    i       i i      i i        i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)6joes
7 Dec 24  ii    i       i i      i i        i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)5WM
7 Dec 24  ii    i       i i      i i        i i   +- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1joes
7 Dec 24  ii    i       i i      i i        i i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3Richard Damon
7 Dec 24  ii    i       i i      i i        i i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2Chris M. Thomasson
8 Dec 24  ii    i       i i      i i        i i     `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Richard Damon
5 Dec 24  ii    i       i i      i i        i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)8FromTheRafters
5 Dec 24  ii    i       i i      i i        i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)5WM
5 Dec 24  ii    i       i i      i i        i  i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)4FromTheRafters
5 Dec 24  ii    i       i i      i i        i  i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3WM
6 Dec 24  ii    i       i i      i i        i  i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2FromTheRafters
6 Dec 24  ii    i       i i      i i        i  i   `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
6 Dec 24  ii    i       i i      i i        i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2Chris M. Thomasson
6 Dec 24  ii    i       i i      i i        i   `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Moebius
5 Dec 24  ii    i       i i      i i        +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)20Richard Damon
5 Dec 24  ii    i       i i      i i        i+* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)18WM
6 Dec 24  ii    i       i i      i i        ii+* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)8Richard Damon
6 Dec 24  ii    i       i i      i i        iii`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)7WM
6 Dec 24  ii    i       i i      i i        iii +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)5joes
6 Dec 24  ii    i       i i      i i        iii i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)4WM
6 Dec 24  ii    i       i i      i i        iii `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Richard Damon
6 Dec 24  ii    i       i i      i i        ii`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)9Chris M. Thomasson
6 Dec 24  ii    i       i i      i i        i`- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Chris M. Thomasson
6 Dec 24  ii    i       i i      i i        `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Chris M. Thomasson
4 Dec 24  ii    i       i i      i `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1WM
4 Dec 24  ii    i       i i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3Ben Bacarisse
3 Dec 24  ii    i       i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)4Jim Burns
2 Dec 24  ii    i       +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2Moebius
2 Dec 24  ii    i       +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2Moebius
2 Dec 24  ii    i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)251FromTheRafters
29 Nov 24  ii    `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Ross Finlayson
29 Nov 24  i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)7Jim Burns
28 Nov 24  `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Ross Finlayson

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