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 : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.math
Date : 08. Nov 2024, 18:05:40
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <1cd9f8e7c9120e79cfb3db241fba9c1d653f3ad1@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
User-Agent : Mozilla Thunderbird
On 11/8/24 11:43 AM, WM wrote:
On 08.11.2024 13:28, Richard Damon wrote:
On 11/8/24 5:18 AM, WM wrote:
 
My understanding of mathematics and geometry is that reordering cannot increase the measure (only reduce it by overlapping). This is a basic axiom which will certainly be agreed to by everybody not conditioned by matheology. But there is also an analytical proof: Every reordering of any finite set of intervals does not increase their measure. The limit of a constant sequence is this constant however.
>
This geometrical consequence of Cantor's theory has, to my knowledge, never been discussed. By the way I got the idea after a posting of yours: Each of {...,-3,-2,-1,0,1,2,3,...} is the midpoint of an interval.
 
which makes the error that the properties of finite objects apply to the infinite objects, which isn't true, and what just breaks your logic.
 The infinite of the real axis is a big supply but an as big drain.
What "drain", the numbers exist.

>
You take it as a given, but that just means that your logic is unable to actually handle the infinite.
 I take it as evident that intervals of the measure 1/5 of the positive real axis will not, by any shuffling, cover the real axis completely, let alone infinitely often. I think who believes this is a deplorable fanatic if not a fool.
 Regards, WM
 
Since 1/5 of infinity isn't a finite measure, you can't use finite logic to handle them.
You are just proving your use of broken logic.

Date Sujet#  Auteur
3 Nov 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers504Jim Burns
4 Nov 24 `* Re: Incompleteness of Cantor's enumeration of the rational numbers503WM
4 Nov 24  `* Re: Incompleteness of Cantor's enumeration of the rational numbers502Jim Burns
4 Nov 24   +* Re: Incompleteness of Cantor's enumeration of the rational numbers480WM
5 Nov 24   i`* Re: Incompleteness of Cantor's enumeration of the rational numbers479Jim 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 numbers469WM
6 Nov 24   i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers468Jim Burns
6 Nov 24   i i +* Re: Incompleteness of Cantor's enumeration of the rational numbers465WM
6 Nov 24   i i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers464Jim Burns
6 Nov 24   i i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers463WM
6 Nov 24   i i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers462Jim Burns
7 Nov 24   i i i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers461WM
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 numbers453Jim Burns
7 Nov 24   i i i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers452WM
8 Nov 24   i i i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers451Jim Burns
8 Nov 24   i i i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers450WM
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 numbers429Jim Burns
9 Nov 24   i i i         `* Re: Incompleteness of Cantor's enumeration of the rational numbers428WM
10 Nov 24   i i i          `* Re: Incompleteness of Cantor's enumeration of the rational numbers427Jim Burns
10 Nov 24   i i i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers426WM
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 numbers388Jim Burns
11 Nov 24   i i i            i`* Re: Incompleteness of Cantor's enumeration of the rational numbers387WM
11 Nov 24   i i i            i `* Re: Incompleteness of Cantor's enumeration of the rational numbers386Jim Burns
11 Nov 24   i i i            i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers385WM
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 numbers377Jim Burns
12 Nov 24   i i i            i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers376WM
12 Nov 24   i i i            i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers375Jim Burns
12 Nov 24   i i i            i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers374WM
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 numbers371Jim Burns
13 Nov 24   i i i            i        `* Re: Incompleteness of Cantor's enumeration of the rational numbers370WM
13 Nov 24   i i i            i         `* Re: Incompleteness of Cantor's enumeration of the rational numbers369Jim Burns
13 Nov 24   i i i            i          `* Re: Incompleteness of Cantor's enumeration of the rational numbers368WM
14 Nov 24   i i i            i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers367Jim 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 numbers360WM
14 Nov 24   i i i            i             +* Re: Incompleteness of Cantor's enumeration of the rational numbers290Jim Burns
15 Nov 24   i i i            i             i`* Re: Incompleteness of Cantor's enumeration of the rational numbers289WM
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 numbers286Jim Burns
15 Nov 24   i i i            i             i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers285WM
15 Nov 24   i i i            i             i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers284Chris 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 numbers279Moebius
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 numbers275Chris M. Thomasson
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 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
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
16 Nov 24   i i i            i             i    i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers258Moebius
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 numbers21Chris M. Thomasson

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