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 : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.math
Date : 14. Jan 2025, 09:47:45
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vm58bh$2b5ia$2@dont-email.me>
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
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On 14.01.2025 00:47, Richard Damon wrote:
On 1/13/25 7:42 AM, WM wrote:
On 13.01.2025 03:54, Richard Damon wrote:
On 1/12/25 5:58 AM, WM wrote:
On 11.01.2025 14:34, joes wrote:
>
1, 2, 3, 4, 5, ..., ω becomes 2, 4, 6, 8, 10, ..., ω, ω+2, ω+4, ..., ω2.
No. There is no x e N such that 2*x >= omega. You have listed two
consecutive infinities on the right.
>
There is a basic law: When a sequence of regular distances is multiplied by 2, then a sequence of regular distances results.
>
Which isn't applicable, since their isn't such a "regular distance"
>
Between all natural numbers, there is a regular distance. When doubled, the new ones do not fit between the old ones and ω because nothing fits between ℕ and ω.
 But omega isn't a natural number, so the space between the ... and omega isn't the same as the space between two consecutive natural numbers.
Maybe. But the space between the natural numbers is doubled while the accessible space remains constant in actual infinity.
 And the distance between the ... and omega *IS* big enough to fit the doubling of all the numbers (without needing to make any new ones).
If there is space, then it is filled before doubling already. Why shouldn't it?
 
>
your starting premise is just
>
to double all numbers which fit between 1 and ω.
 Which are still just the even numbers between 1 and omega.
∀n ∈ ℕ: 2n > n. All numbers are doubled. Their number remains the same (not only the cardinality, but the reality). Half of all are deleted. Half are new.

correct understanding that all between 1 and ω is available for doubling and nothing can be inserted.
 And nothing NEEDS to be inserted.
It cannot. Therefore half of the results is larger than ω.
Regards, WM

Date Sujet#  Auteur
27 Nov 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1050WM
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)1047Jim Burns
28 Nov 24  +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1045WM
28 Nov 24  i+* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1037joes
28 Nov 24  ii`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1036WM
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)1031FromTheRafters
28 Nov 24  ii  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1030WM
28 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)1027FromTheRafters
29 Nov 24  ii    +* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1025WM
29 Nov 24  ii    i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1024FromTheRafters
29 Nov 24  ii    i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1023WM
29 Nov 24  ii    i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1022FromTheRafters
30 Nov 24  ii    i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1021WM
30 Nov 24  ii    i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1020FromTheRafters
30 Nov 24  ii    i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1019WM
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)1008Chris 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)59Chris M. Thomasson
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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
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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
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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
5 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)913FromTheRafters
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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