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 : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.math
Date : 07. Nov 2024, 20:33:09
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vgj4lk$2ova9$3@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14
User-Agent : Mozilla Thunderbird
On 07.11.2024 20:06, Jim Burns wrote:
 > On 11/7/2024 3:46 AM, WM wrote:
 >> That means by clever reordering them
 >> you can cover the whole positive axis
 >> except "boundaries".
 >
 > Yes.
 > In that clever re.ordering, not scrunched together,
 > the whole positive axis
 > is in the ε.cover or
 > in the boundary of the ε.cover.
It is impossible however to cover the real axis (even many times) by the intervals
  J(n) = [n - 1/10, n + 1/10].
No boundaries are involved because every interval of length 1/5 contains infinitely many rationals and therefore is essentially covered by infinitely many intervals of length 1/5 - if Cantor is right.
Regards, WM

Date Sujet#  Auteur
4 Nov 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers501Jim Burns
4 Nov 24 `* Re: Incompleteness of Cantor's enumeration of the rational numbers500WM
4 Nov 24  `* Re: Incompleteness of Cantor's enumeration of the rational numbers499Jim Burns
4 Nov 24   +* Re: Incompleteness of Cantor's enumeration of the rational numbers474WM
5 Nov 24   i`* Re: Incompleteness of Cantor's enumeration of the rational numbers473Jim 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
6 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 numbers463WM
6 Nov 24   i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers462Jim Burns
6 Nov 24   i i +* Re: Incompleteness of Cantor's enumeration of the rational numbers459WM
6 Nov 24   i i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers458Jim Burns
6 Nov 24   i i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers457WM
6 Nov 24   i i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers456Jim Burns
7 Nov 24   i i i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers455WM
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 numbers447Jim Burns
7 Nov 24   i i i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers446WM
8 Nov 24   i i i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers445Jim Burns
8 Nov 24   i i i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers444WM
8 Nov 24   i i i        +* Re: Incompleteness of Cantor's enumeration of the rational numbers13Richard Damon
8 Nov 24   i i i        i`* Re: Incompleteness of Cantor's enumeration of the rational numbers12WM
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 numbers9joes
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
10 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 numbers1WM
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 numbers428Jim Burns
9 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 numbers426Jim Burns
10 Nov 24   i i i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers425WM
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 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 numbers385Jim Burns
11 Nov 24   i i i            i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers384WM
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 numbers376Jim Burns
12 Nov 24   i i i            i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers375WM
12 Nov 24   i i i            i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers374Jim Burns
12 Nov 24   i i i            i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers373WM
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 numbers370Jim Burns
13 Nov 24   i i i            i        `* Re: Incompleteness of Cantor's enumeration of the rational numbers369WM
13 Nov 24   i i i            i         `* Re: Incompleteness of Cantor's enumeration of the rational numbers368Jim Burns
13 Nov 24   i i i            i          `* Re: Incompleteness of Cantor's enumeration of the rational numbers367WM
14 Nov 24   i i i            i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers366Jim 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 numbers359WM
14 Nov 24   i i i            i             +* Re: Incompleteness of Cantor's enumeration of the rational numbers289Jim Burns
15 Nov 24   i i i            i             i`* Re: Incompleteness of Cantor's enumeration of the rational numbers288WM
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 numbers285Jim Burns
15 Nov 24   i i i            i             i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers284WM
15 Nov 24   i i i            i             i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers283Chris M. Thomasson
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 numbers278Moebius
16 Nov 24   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+* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
16 Nov 24   i i i            i             i    ii`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
16 Nov 24   i i i            i             i    i`* Re: Incompleteness of Cantor's enumeration of the rational numbers274Chris M. Thomasson
16 Nov 24   i i i            i             i    i `* Re: Incompleteness of Cantor's enumeration of the rational numbers273Chris M. Thomasson
16 Nov 24   i i i            i             i    i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Chris M. Thomasson
16 Nov 24   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  +* Re: Incompleteness of Cantor's enumeration of the rational numbers13FromTheRafters
16 Nov 24   i i i            i             i    i  i`* Re: Incompleteness of Cantor's enumeration of the rational numbers12Chris M. Thomasson
16 Nov 24   i i i            i             i    i  i +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
16 Nov 24   i i i            i             i    i  i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
17 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 i`* Re: Incompleteness of Cantor's enumeration of the rational numbers6Chris M. Thomasson
17 Nov 24   i i i            i             i    i  i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers5Moebius
17 Nov 24   i i i            i             i    i  i i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
17 Nov 24   i i i            i             i    i  i i  i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
17 Nov 24   i i i            i             i    i  i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers2Chris M. Thomasson
17 Nov 24   i i i            i             i    i  i `* Re: Incompleteness of Cantor's enumeration of the rational numbers2FromTheRafters
16 Nov 24   i i i            i             i    i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers257Moebius
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
10 Nov 24   i i i            `* Re: Incompleteness of Cantor's enumeration of the rational numbers36Chris M. Thomasson
6 Nov 24   i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (opinions)2Ross Finlayson
6 Nov 24   i `* Re: Incompleteness of Cantor's enumeration of the rational numbers5WM
4 Nov 24   `* Re: Incompleteness of Cantor's enumeration of the rational numbers24Chris M. Thomasson

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