Re: The non-existence of "dark numbers"

Liste des GroupesRevenir à s math 
Sujet : Re: The non-existence of "dark numbers"
De : noreply (at) *nospam* example.org (joes)
Groupes : sci.math
Date : 15. Mar 2025, 17:56:12
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <e21febc3602fe07d39ab0ed6edb071668cccc4d1@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
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Am Sat, 15 Mar 2025 17:49:49 +0100 schrieb WM:
On 15.03.2025 12:32, joes wrote:
Am Sat, 15 Mar 2025 09:56:31 +0100 schrieb WM:
On 15.03.2025 00:11, Alan Mackenzie wrote:
WM <wolfgang.mueckenheim@tha.de> wrote:
>
ℕ_def contains all numbers the subtraction of which from ℕ does not
result in the empty set.
What does "which" refer to?
It refers to the numbers. An Englishman should comprehend that.
It could also have referred to the set. But in this case, N_def=N.
ℕ_def contains all numbers the subtraction of which from ℕ does not
result in the empty set.
For every number in N, if you subtract that number, a nonempty set
remains. Of course, if you subtract all of them, nothing does.

ℕ contains all numbers the subtraction of which from ℕ does result in
the empty set.
No element of N, subtracted from N, leaves the empty set (because N
contains more than one element).

To N_def or to a member of the "all numbers"?
That is one and the same.
No. N_def is not a number.
ℕ_def contains all numbers the subtraction of which from ℕ does not
result in the empty set.
Yes, N_def is a set.
--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.

Date Sujet#  Auteur
12 Mar 25 * The existence of dark numbers proven by the thinned out harmonic series451WM
12 Mar 25 `* Re: The existence of dark numbers proven by the thinned out harmonic series450Alan Mackenzie
12 Mar 25  `* Re: The existence of dark numbers proven by the thinned out harmonic series449WM
12 Mar 25   `* The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]448Alan Mackenzie
12 Mar 25    +* Re: The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]444WM
12 Mar 25    i+* Re: The non-existence of "dark numbers"414Alan Mackenzie
12 Mar 25    ii`* Re: The non-existence of "dark numbers"413WM
12 Mar 25    ii `* Re: The non-existence of "dark numbers"412Alan Mackenzie
12 Mar 25    ii  +* Re: The non-existence of "dark numbers"6Moebius
13 Mar 25    ii  i+- Re: The non-existence of "dark numbers"1WM
13 Mar 25    ii  i`* Re: The non-existence of "dark numbers"4Alan Mackenzie
13 Mar 25    ii  i `* Re: The non-existence of "dark numbers"3Moebius
13 Mar 25    ii  i  `* Re: The non-existence of "dark numbers"2WM
13 Mar 25    ii  i   `- Re: The non-existence of "dark numbers"1joes
13 Mar 25    ii  +* Re: The non-existence of "dark numbers"401WM
13 Mar 25    ii  i+* Re: The non-existence of "dark numbers"399Alan Mackenzie
13 Mar 25    ii  ii+* Re: The non-existence of "dark numbers"397WM
13 Mar 25    ii  iii+* Re: The non-existence of "dark numbers"3joes
13 Mar 25    ii  iiii`* Re: The non-existence of "dark numbers"2WM
14 Mar 25    ii  iiii `- Re: The non-existence of "dark numbers"1joes
13 Mar 25    ii  iii`* Re: The non-existence of "dark numbers"393Alan Mackenzie
14 Mar 25    ii  iii `* Re: The non-existence of "dark numbers"392WM
14 Mar 25    ii  iii  +* Re: The non-existence of "dark numbers"7FromTheRafters
14 Mar 25    ii  iii  i`* Re: The non-existence of "dark numbers"6WM
14 Mar 25    ii  iii  i `* Re: The non-existence of "dark numbers"5FromTheRafters
14 Mar 25    ii  iii  i  `* Re: The non-existence of "dark numbers"4WM
15 Mar 25    ii  iii  i   `* Re: The non-existence of "dark numbers"3FromTheRafters
15 Mar 25    ii  iii  i    +- Re: The non-existence of "dark numbers" (thread too long, nothing in it)1Ross Finlayson
15 Mar 25    ii  iii  i    `- Re: The non-existence of "dark numbers"1WM
14 Mar 25    ii  iii  +* Re: The non-existence of "dark numbers"383Alan Mackenzie
14 Mar 25    ii  iii  i`* Re: The non-existence of "dark numbers"382WM
14 Mar 25    ii  iii  i +* Re: The non-existence of "dark numbers"380Alan Mackenzie
14 Mar 25    ii  iii  i i`* Re: The non-existence of "dark numbers"379WM
15 Mar 25    ii  iii  i i +* Re: The non-existence of "dark numbers"371Alan Mackenzie
15 Mar 25    ii  iii  i i i`* Re: The non-existence of "dark numbers"370WM
15 Mar 25    ii  iii  i i i +* Re: The non-existence of "dark numbers"4joes
15 Mar 25    ii  iii  i i i i`* Re: The non-existence of "dark numbers"3WM
15 Mar 25    ii  iii  i i i i `* Re: The non-existence of "dark numbers"2joes
15 Mar 25    ii  iii  i i i i  `- Re: The non-existence of "dark numbers"1WM
15 Mar 25    ii  iii  i i i +* Re: The non-existence of "dark numbers"362Alan Mackenzie
15 Mar 25    ii  iii  i i i i`* Re: The non-existence of "dark numbers"361WM
16 Mar 25    ii  iii  i i i i +* Re: The non-existence of "dark numbers"356Alan Mackenzie
16 Mar 25    ii  iii  i i i i i`* Re: The non-existence of "dark numbers"355WM
16 Mar 25    ii  iii  i i i i i +* Re: The non-existence of "dark numbers"268Jim Burns
16 Mar 25    ii  iii  i i i i i i`* Re: The non-existence of "dark numbers"267WM
16 Mar 25    ii  iii  i i i i i i `* Re: The non-existence of "dark numbers"266Jim Burns
16 Mar 25    ii  iii  i i i i i i  `* Re: The non-existence of "dark numbers"265WM
16 Mar 25    ii  iii  i i i i i i   `* Re: The non-existence of "dark numbers"264Jim Burns
16 Mar 25    ii  iii  i i i i i i    `* Re: The non-existence of "dark numbers"263WM
17 Mar 25    ii  iii  i i i i i i     `* Re: The non-existence of "dark numbers"262Jim Burns
17 Mar 25    ii  iii  i i i i i i      `* Re: The non-existence of "dark numbers"261WM
17 Mar 25    ii  iii  i i i i i i       `* Re: The non-existence of "dark numbers"260Jim Burns
17 Mar 25    ii  iii  i i i i i i        `* Re: The non-existence of "dark numbers"259WM
17 Mar 25    ii  iii  i i i i i i         `* Re: The non-existence of "dark numbers"258Jim Burns
18 Mar 25    ii  iii  i i i i i i          `* Re: The non-existence of "dark numbers"257WM
18 Mar 25    ii  iii  i i i i i i           `* Re: The non-existence of "dark numbers"256Jim Burns
18 Mar 25    ii  iii  i i i i i i            `* Re: The non-existence of "dark numbers"255WM
19 Mar 25    ii  iii  i i i i i i             `* Re: The non-existence of "dark numbers"254Jim Burns
19 Mar 25    ii  iii  i i i i i i              `* Re: The non-existence of "dark numbers"253WM
19 Mar 25    ii  iii  i i i i i i               `* Re: The non-existence of "dark numbers"252Jim Burns
20 Mar 25    ii  iii  i i i i i i                `* Re: The non-existence of "dark numbers"251WM
20 Mar 25    ii  iii  i i i i i i                 `* Re: The non-existence of "dark numbers"250Jim Burns
20 Mar 25    ii  iii  i i i i i i                  `* Re: The non-existence of "dark numbers"249WM
20 Mar 25    ii  iii  i i i i i i                   `* Re: The non-existence of "dark numbers"248Jim Burns
21 Mar 25    ii  iii  i i i i i i                    `* Re: The non-existence of "dark numbers"247WM
21 Mar 25    ii  iii  i i i i i i                     `* Re: The non-existence of "dark numbers"246Jim Burns
21 Mar 25    ii  iii  i i i i i i                      `* Re: The non-existence of "dark numbers"245WM
21 Mar 25    ii  iii  i i i i i i                       +* The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]183Alan Mackenzie
21 Mar 25    ii  iii  i i i i i i                       i+* Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]40Moebius
21 Mar 25    ii  iii  i i i i i i                       ii+* Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]37Moebius
21 Mar 25    ii  iii  i i i i i i                       iii+* Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]2Moebius
21 Mar 25    ii  iii  i i i i i i                       iiii`- Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]1Moebius
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21 Mar 25    ii  iii  i i i i i i                       iii +* Re: The reality of sets, on a scale of 1 to 1032Moebius
22 Mar 25    ii  iii  i i i i i i                       iii i+- Re: The reality of sets, on a scale of 1 to 101Ross Finlayson
22 Mar 25    ii  iii  i i i i i i                       iii i+* Re: The reality of sets, on a scale of 1 to 1029Ralf Bader
22 Mar 25    ii  iii  i i i i i i                       iii ii`* Re: The reality of sets, on a scale of 1 to 1028Moebius
22 Mar 25    ii  iii  i i i i i i                       iii ii +* Re: The reality of sets, on a scale of 1 to 102Moebius
22 Mar 25    ii  iii  i i i i i i                       iii ii i`- Re: The reality of sets, on a scale of 1 to 101Moebius
23 Mar 25    ii  iii  i i i i i i                       iii ii `* Re: The reality of sets, on a scale of 1 to 1025Ross Finlayson
23 Mar 25    ii  iii  i i i i i i                       iii ii  `* Re: The reality of sets, on a scale of 1 to 1024Jim Burns
23 Mar 25    ii  iii  i i i i i i                       iii ii   `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)23Ross Finlayson
24 Mar 25    ii  iii  i i i i i i                       iii ii    +* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)19Chris M. Thomasson
24 Mar 25    ii  iii  i i i i i i                       iii ii    i`* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)18Jim Burns
24 Mar 25    ii  iii  i i i i i i                       iii ii    i +* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)11Ross Finlayson
24 Mar 25    ii  iii  i i i i i i                       iii ii    i i`* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)10Jim Burns
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)9Ross Finlayson
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i  +* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)3Jim Burns
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i  i`* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)2Ross Finlayson
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i  i `- Re: The reality of sets, on a scale of 1 to 10 (theory of theories)1Jim Burns
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i  `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)5Jim Burns
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i   `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)4Ross Finlayson
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i    `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)3Jim Burns
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i     `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)2Ross Finlayson
25 Mar 25    ii  iii  i i i i i i                       iii ii    i i      `- Re: The reality of sets, on a scale of 1 to 10 (theory of theories)1Jim Burns
26 Mar 25    ii  iii  i i i i i i                       iii ii    i `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)6Chris M. Thomasson
27 Mar 25    ii  iii  i i i i i i                       iii ii    i  `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)5Jim Burns
27 Mar 25    ii  iii  i i i i i i                       iii ii    i   `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)4FromTheRafters
27 Mar 25    ii  iii  i i i i i i                       iii ii    i    +- Re: The reality of sets, on a scale of 1 to 10 (theory of theories)1Jim Burns
27 Mar 25    ii  iii  i i i i i i                       iii ii    i    `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)2Ross Finlayson
27 Mar 25    ii  iii  i i i i i i                       iii ii    i     `- Re: The reality of sets, on a scale of 1 to 10 (theory of theories)1Ross Finlayson
24 Mar 25    ii  iii  i i i i i i                       iii ii    `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)3Jim Burns
22 Mar 25    ii  iii  i i i i i i                       iii i`- Re: The reality of sets, on a scale of 1 to 101WM
22 Mar 25    ii  iii  i i i i i i                       iii `- Re: The reality of sets, on a scale of 1 to 101WM
22 Mar 25    ii  iii  i i i i i i                       ii`* Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]2WM
22 Mar 25    ii  iii  i i i i i i                       i`* Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]142WM
21 Mar 25    ii  iii  i i i i i i                       +* Re: The non-existence of "dark numbers"3FromTheRafters
22 Mar 25    ii  iii  i i i i i i                       `* Re: The non-existence of "dark numbers"58Jim Burns
16 Mar 25    ii  iii  i i i i i +* Re: The non-existence of "dark numbers"85Alan Mackenzie
16 Mar 25    ii  iii  i i i i i `- Re: The non-existence of "dark numbers"1joes
16 Mar 25    ii  iii  i i i i `* Re: The non-existence of "dark numbers"4joes
15 Mar 25    ii  iii  i i i `* Re: The non-existence of "dark numbers"3Chris M. Thomasson
15 Mar 25    ii  iii  i i `* Re: The non-existence of "dark numbers"7joes
14 Mar 25    ii  iii  i `- Re: The non-existence of "dark numbers"1joes
14 Mar 25    ii  iii  `- Re: The non-existence of "dark numbers"1joes
14 Mar 25    ii  ii`- Re: The non-existence of "dark numbers"1Chris M. Thomasson
13 Mar 25    ii  i`- Re: The non-existence of "dark numbers"1joes
13 Mar 25    ii  `* Re: The non-existence of "dark numbers"4Ben Bacarisse
12 Mar 25    i`* Re: The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]29Jim Burns
12 Mar 25    +* Re: The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]2FromTheRafters
12 Mar 25    `- Re: The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]1Jim Burns

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