Re: Incompleteness of Cantor's enumeration of the rational numbers

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Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.math
Date : 23. Nov 2024, 06:32:09
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vhrpcp$1j7o6$4@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 25 26 27 28
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Am 23.11.2024 um 06:18 schrieb Moebius:
On 22.11.2024 16:11, joes wrote:
Am Fri, 22 Nov 2024 15:51:11 +0100 schrieb WM:
 
the sets of naturals and of prime numbers [can] cover each other.
>
As it should. You can give each prime an index.
 Indeed! The two formulas
 | p(1) = min P
| p(n+1) = min {p e P : p > p(n)}   (for all n e IN)
 (recursively) define the function p: IN --> P. Where IN is the set of all natural numbers and P is the set of all prime numbers.
 Hint: p(1) = 2, p(2) = 3, p(3) = 5, ...
 Actually, if p e P, then there is an (index) n e IN such that p(n) = p.
 (It's easy to prove that p: IN --> P is a bijection.)
p(n) is the n-th prime number in the sequence of prime numbers ordered by size.
.
.
.

Date Sujet#  Auteur
3 Nov 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers505Jim Burns
4 Nov 24 `* Re: Incompleteness of Cantor's enumeration of the rational numbers504WM
4 Nov 24  `* Re: Incompleteness of Cantor's enumeration of the rational numbers503Jim Burns
4 Nov 24   +* Re: Incompleteness of Cantor's enumeration of the rational numbers481WM
5 Nov 24   i`* Re: Incompleteness of Cantor's enumeration of the rational numbers480Jim Burns
5 Nov 24   i +* Re: Incompleteness of Cantor's enumeration of the rational numbers4Jim Burns
5 Nov 24   i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (re-Vitali-ized)3Ross Finlayson
5 Nov 24   i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (re-Vitali-ized)2Ross Finlayson
5 Nov 24   i i  `- Re: Incompleteness of Cantor's enumeration of the rational numbers (re-Vitali-ized)1Chris M. Thomasson
6 Nov 24   i +* Re: Incompleteness of Cantor's enumeration of the rational numbers470WM
6 Nov 24   i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers469Jim Burns
6 Nov 24   i i +* Re: Incompleteness of Cantor's enumeration of the rational numbers466WM
6 Nov 24   i i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers465Jim Burns
6 Nov 24   i i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers464WM
6 Nov 24   i i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers463Jim Burns
7 Nov 24   i i i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers462WM
7 Nov 24   i i i    +* Re: Incompleteness of Cantor's enumeration of the rational numbers7Jim Burns
7 Nov 24   i i i    i`* Re: Incompleteness of Cantor's enumeration of the rational numbers6WM
7 Nov 24   i i i    i `* Re: Incompleteness of Cantor's enumeration of the rational numbers5Jim Burns
7 Nov 24   i i i    i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers4WM
7 Nov 24   i i i    i   +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Jim Burns
7 Nov 24   i i i    i   i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
7 Nov 24   i i i    i   `- Re: Incompleteness of Cantor's enumeration of the rational numbers1Chris M. Thomasson
7 Nov 24   i i i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers454Jim Burns
7 Nov 24   i i i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers453WM
8 Nov 24   i i i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers452Jim Burns
8 Nov 24   i i i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers451WM
8 Nov 24   i i i        +* Re: Incompleteness of Cantor's enumeration of the rational numbers18Richard Damon
8 Nov 24   i i i        i`* Re: Incompleteness of Cantor's enumeration of the rational numbers17WM
8 Nov 24   i i i        i +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Richard Damon
9 Nov 24   i i i        i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
8 Nov 24   i i i        i `* Re: Incompleteness of Cantor's enumeration of the rational numbers14joes
8 Nov 24   i i i        i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers7Moebius
8 Nov 24   i i i        i  i`* Re: Incompleteness of Cantor's enumeration of the rational numbers6Moebius
9 Nov 24   i i i        i  i `* Re: Incompleteness of Cantor's enumeration of the rational numbers5WM
9 Nov 24   i i i        i  i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers4Chris M. Thomasson
9 Nov 24   i i i        i  i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers3Moebius
10 Nov 24   i i i        i  i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers2WM
10 Nov 24   i i i        i  i     `- Re: Incompleteness of Cantor's enumeration of the rational numbers1Chris M. Thomasson
9 Nov 24   i i i        i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers6WM
26 Dec 24   i i i        i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers5Chris M. Thomasson
26 Dec 24   i i i        i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers4Moebius
27 Dec 24   i i i        i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers3Chris M. Thomasson
27 Dec 24   i i i        i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
28 Dec 24   i i i        i       `- Re: Incompleteness of Cantor's enumeration of the rational numbers1Chris M. Thomasson
8 Nov 24   i i i        +* Re: Incompleteness of Cantor's enumeration of the rational numbers (doubling-spaces)2Ross Finlayson
8 Nov 24   i i i        i`- Re: Incompleteness of Cantor's enumeration of the rational numbers (doubling-spaces)1Ross Finlayson
8 Nov 24   i i i        `* Re: Incompleteness of Cantor's enumeration of the rational numbers430Jim Burns
9 Nov 24   i i i         `* Re: Incompleteness of Cantor's enumeration of the rational numbers429WM
10 Nov 24   i i i          `* Re: Incompleteness of Cantor's enumeration of the rational numbers428Jim Burns
10 Nov 24   i i i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers427WM
10 Nov 24   i i i            +- Re: Incompleteness of Cantor's enumeration of the rational numbers (exponential)1Ross Finlayson
10 Nov 24   i i i            +* Re: Incompleteness of Cantor's enumeration of the rational numbers389Jim Burns
11 Nov 24   i i i            i`* Re: Incompleteness of Cantor's enumeration of the rational numbers388WM
11 Nov 24   i i i            i `* Re: Incompleteness of Cantor's enumeration of the rational numbers387Jim Burns
11 Nov 24   i i i            i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers386WM
11 Nov 24   i i i            i   +* Re: Incompleteness of Cantor's enumeration of the rational numbers5FromTheRafters
12 Nov 24   i i i            i   i`* Re: Incompleteness of Cantor's enumeration of the rational numbers4WM
12 Nov 24   i i i            i   i +- Re: Incompleteness of Cantor's enumeration of the rational numbers1FromTheRafters
12 Nov 24   i i i            i   i `* Re: Incompleteness of Cantor's enumeration of the rational numbers2joes
12 Nov 24   i i i            i   i  `- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
12 Nov 24   i i i            i   +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Jim Burns
12 Nov 24   i i i            i   i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
12 Nov 24   i i i            i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers378Jim Burns
12 Nov 24   i i i            i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers377WM
12 Nov 24   i i i            i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers376Jim Burns
12 Nov 24   i i i            i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers375WM
13 Nov 24   i i i            i       +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Jim Burns
13 Nov 24   i i i            i       i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
13 Nov 24   i i i            i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers372Jim Burns
13 Nov 24   i i i            i        `* Re: Incompleteness of Cantor's enumeration of the rational numbers371WM
13 Nov 24   i i i            i         `* Re: Incompleteness of Cantor's enumeration of the rational numbers370Jim Burns
13 Nov 24   i i i            i          `* Re: Incompleteness of Cantor's enumeration of the rational numbers369WM
14 Nov 24   i i i            i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers368Jim Burns
14 Nov 24   i i i            i            +* Re: Incompleteness of Cantor's enumeration of the rational numbers6FromTheRafters
14 Nov 24   i i i            i            i`* Re: Incompleteness of Cantor's enumeration of the rational numbers5Jim Burns
14 Nov 24   i i i            i            i +* Re: Incompleteness of Cantor's enumeration of the rational numbers3Ross Finlayson
15 Nov 24   i i i            i            i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (research)2Ross Finlayson
15 Nov 24   i i i            i            i i `- Re: Incompleteness of Cantor's enumeration of the rational numbers (research)1Ross Finlayson
14 Nov 24   i i i            i            i `- Re: Incompleteness of Cantor's enumeration of the rational numbers1FromTheRafters
14 Nov 24   i i i            i            `* Re: Incompleteness of Cantor's enumeration of the rational numbers361WM
14 Nov 24   i i i            i             +* Re: Incompleteness of Cantor's enumeration of the rational numbers291Jim Burns
15 Nov 24   i i i            i             i`* Re: Incompleteness of Cantor's enumeration of the rational numbers290WM
15 Nov 24   i i i            i             i +* Re: Incompleteness of Cantor's enumeration of the rational numbers2joes
15 Nov 24   i i i            i             i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
15 Nov 24   i i i            i             i `* Re: Incompleteness of Cantor's enumeration of the rational numbers287Jim Burns
15 Nov 24   i i i            i             i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers286WM
15 Nov 24   i i i            i             i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers285Chris M. Thomasson
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16 Nov 24   i i i            i             i    i `* Re: Incompleteness of Cantor's enumeration of the rational numbers275Chris M. Thomasson
16 Nov 24   i i i            i             i    i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Chris M. Thomasson
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16 Nov 24   i i i            i             i    i  i`* Re: Incompleteness of Cantor's enumeration of the rational numbers12Chris M. Thomasson
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16 Nov 24   i i i            i             i    i  i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
16 Nov 24   i i i            i             i    i  i +* Re: Incompleteness of Cantor's enumeration of the rational numbers7Moebius
17 Nov 24   i i i            i             i    i  i `* Re: Incompleteness of Cantor's enumeration of the rational numbers2FromTheRafters
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16 Nov 24   i i i            i             i    +- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
16 Nov 24   i i i            i             i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
14 Nov 24   i i i            i             `* Re: Incompleteness of Cantor's enumeration of the rational numbers69Jim Burns
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