Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]
Groups > sci.math > #602228 > unrolled thread
| Started by | Peter Peters <pp1585024@gmail.com> |
|---|---|
| First post | 2023-06-14 03:35 -0700 |
| Last post | 2023-07-05 07:48 -0700 |
| Articles | 20 on this page of 165 — 16 participants |
Back to article view | Back to sci.math
The mathematical constraints of set theory Peter Peters <pp1585024@gmail.com> - 2023-06-14 03:35 -0700
Re: The mathematical constraints of set theory Guckie <alberstein@freenet.de> - 2023-06-14 16:36 +0300
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 07:45 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 08:20 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 16:30 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 11:45 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:13 +0100
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 18:07 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 06:24 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 05:50 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-15 17:36 +0100
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 13:51 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:19 +0100
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 04:44 -0700
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 10:39 -0700
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-27 09:00 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:13 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 15:45 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-14 10:08 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:44 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 08:03 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 08:29 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-16 09:03 -0700
Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-16 13:30 -0400
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 12:08 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-17 06:26 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-17 09:18 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 05:57 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-18 07:01 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:13 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-17 10:09 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-17 10:58 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:09 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-18 09:40 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 05:05 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:15 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:22 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:38 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:40 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:24 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 09:11 -0700
Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 11:27 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 11:44 -0700
Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 12:07 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 12:12 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-20 06:43 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-20 06:53 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-19 16:47 +0100
Re: The mathematical constraints of set theory Dieter Heidorn <d.heidorn@t-online.de> - 2023-06-19 20:11 +0200
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 00:08 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:49 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:35 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:09 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:19 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 01:13 +0100
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 18:35 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 03:04 +0100
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:52 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:54 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 15:42 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-27 08:39 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 02:43 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 04:32 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 15:16 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 07:48 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 16:43 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:49 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-29 09:59 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-30 13:04 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-30 18:09 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:18 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:25 -0700
Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-30 18:53 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 16:42 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-01 10:19 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-01 14:06 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:52 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 09:48 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 10:39 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 13:45 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 14:09 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-02 14:08 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 07:01 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-03 13:09 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-04 08:33 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-04 18:43 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:50 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 10:39 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 08:45 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 13:14 -0400
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-06 06:27 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-09 06:41 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-09 07:58 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:40 -0700
Re: The mathematical constraints of set theory Tom Bola <Tom@bolamail.etc> - 2023-07-01 20:23 +0200
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 11:44 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:43 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 08:42 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 06:52 -0700
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-07-01 11:56 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:34 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 20:21 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:46 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:11 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 08:20 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:18 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 07:12 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:45 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:38 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:39 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:04 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-19 09:34 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:44 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 13:31 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:37 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:03 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:05 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:53 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:50 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-21 07:37 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:13 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 20:34 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:59 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-21 11:58 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:19 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-22 12:30 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 10:38 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 20:18 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:06 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:17 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:24 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:16 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-15 09:50 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 14:00 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:28 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:50 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-18 02:13 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:19 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 01:26 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 07:09 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 15:38 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 12:32 -0700
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-20 14:05 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-21 04:43 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:33 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:56 +0100
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-17 18:34 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-14 16:50 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-14 20:19 -0400
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 17:08 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:45 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-16 14:58 -0400
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 18:56 -0400
Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-19 08:37 -0700
Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-23 11:16 -0700
Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 00:23 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:54 -0700
Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 09:36 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-06 05:29 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-09 08:09 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:42 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 04:14 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 07:27 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 07:57 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-05 07:48 -0700
Page 6 of 9 — ← Prev page 1 2 3 4 5 [6] 7 8 9 Next page →
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-28 09:34 -0700 |
| Message-ID | <fa09a373-9f84-4750-b695-5278b22f3a43n@googlegroups.com> |
| In reply to | #603335 |
Ben Bacarisse schrieb am Montag, 26. Juni 2023 um 16:42:30 UTC+2:
> What matters is what he means, not what I mean!
Very good.
> What he means will vary
> from day to day
No, you seem to fail it at all.
> > Hint: There he even denied that f(n) = n (f: IN --> IN) is a bijective
> > function from IN onto IN. Reason: There are no bijections between
> > infinite sets. ("They are not possible ") Period.
Most numbers are dark.
> I've also already had this discussion (more than once). For example:
>
> WM: k = (m + n - 1)(m + n - 2)/2 + m.
>
> Me: I.e. k(n,m) is a bijection from NxN to N, a fact provable by any
> student who has read your textbook. Do you agree that such a student
> could prove this fact?
>
> WM: Of course.
Potential infinity.
> That depends on what he means by a set and by a bjection today! k is
> provably bijective or it does not exist. Take you pick.
Claim: All positive fractions
1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
...
can be indexed by the Cantor function k = (m + n - 1)(m + n - 2)/2 + m which attaches the index k to the fraction m/n in Cantor's sequence
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, ... .
Its terms can be represented by matrices. When we attach all indeXes k = 1, 2, 3, ..., for clarity represented by X, to the integer fractions m/1 and indicate missing indexes by hOles O, then we get the matrix M(0) as starting position:
XOOO... XXOO... XXOO... XXXO... ... XXXX...
XOOO... OOOO... XOOO... XOOO... ... XXXX...
XOOO... XOOO... OOOO... OOOO... ... XXXX...
XOOO... XOOO... XOOO... OOOO... ... XXXX...
... ... ... ... ...
M(0) M(2) M(3) M(4) M(∞)
M(1) is the same as M(0) because index 1 remains at 1/1. In M(2) index 2 from 2/1 has been attached to 1/2. In M(3) index 3 from 3/1 has been attached to 2/1. In M(4) index 4 from 4/1 has been attached to 1/3. Successively all fractions of the sequence get indexed. In the limit, denoted by M(∞), we see no fraction without index remaining. Note that the only difference to Cantor's enumeration is that Cantor does not render account for the source of the indices.
Every X, representing the index k, when taken from its present fraction m/n, is replaced by the O taken from the fraction to be indexed by this k. Its last carrier m/n will be indexed later by another index. Important is that, when continuing, no O can leave the matrix as long as any index X blocks the only possible drain, i.e., the first column. And if leaving, where should it settle?
As long as indexes are in the drain, no O has left. The presence of all O indicates that almost all fractions are not indexed. And after all indexes have been issued and the drain has become free, no indexes are available which could index the remaining matrix elements, yet covered by O.
It should go without saying that by rearranging the X of M(0) never a complete covering can be realized. Lossless transpositions cannot suffer losses. The limit matrix M(∞) only shows what should have happened when all fractions were indexed. Logic proves that this cannot have happened by exchanges. The only explanation for finally seeing M(∞) is that there are invisible matrix positions, existing already at the start. Obviously by exchanging O and X no O can leave the matrix, but the O can disappear by moving without end, from visible to invisible positions.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-25 20:21 -0700 |
| Message-ID | <9402c975-c30f-4d83-9788-ab2745cc9951n@googlegroups.com> |
| In reply to | #603292 |
On Monday, June 26, 2023 at 2:14:01 AM UTC+2, Ben Bacarisse wrote: > ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m > ∀i ∃n,m such that k(n,m) = i > > are both trivially provable. There are no pairs of naturals without an index. Seems that you didn't get my point. These two statements do not ensure that "[t]here are no pairs of naturals without an index" but that there is no "index" (i.e. natural number) without an unique pair of natural numbers which is mapped on it (by k). [They imply that k is invertible.] That "[t]here are no pairs of naturals without 'an index' [if so]" is already ensured by the fact that k is defined with IN x IN as its domain. YES, it is braindead to claim that there are pairs (i, j) e IN x IN which are NOT mapped on some natural number by k (given your definition for k). But this is exactly what Mückenhime does: BB: This is a one-to-one correspondence between the fractions and the naturals WM: No. That is true only for visible numbers. Most fractions remain without index [since they are not visible]. I'll just leave it here. (EOD)
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-28 09:46 -0700 |
| Message-ID | <6264e4ef-f84a-4b45-8647-2e127af284fen@googlegroups.com> |
| In reply to | #603292 |
Ben Bacarisse schrieb am Montag, 26. Juni 2023 um 02:14:01 UTC+2:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
> > Ben Bacarisse schrieb am Freitag, 23. Juni 2023 um 03:36:02 UTC+2:
> >> WM <askas...@gmail.com> writes:
> >
> >> > It is not correct,
> >> Which bit is not correct
> >> (A) This is a one-to-one correspondence between the fractions and the
> >> naturals
> >
> > No. That is true only for visible numbers. Most fractions remain
> > without index.
> ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m
> ∀i ∃n,m such that k(n,m) = i
>
> are both trivially provable. There are no pairs of naturals without an
> index.
That holds for all definable natnumbers and definable fractions. Both are opotentially infinite collections.
>
> >> (C) You know that k(m,n) associates a unique index with every pair,
> >
> > No, the O remain without index.
> ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m
> ∀i ∃n,m such that k(n,m) = i
>
> are trivially provable.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo is also trivially provable. Why do you think to cover all n including the ℵo beyond every n?
> You can't insist that there are some numbers in
> N about which inductive proofs don't apply because of how N is defined.
ℕ_def, a potentially infinite collection, is defined by Peano. Not Cantor's ℕ. All natnumbers are natnumbers, but the dark ones have no discernible order. Therefore we cannot identify a last one. But it is clear that before zero there is a "last" unit fractions. We can inder this from the fct that at zero NUF(x) = 0 and at eps NUF(x) = ℵo. The increase from 0 to ℵo requires belief in mystery or a 1, 2, 3, ... .
> You don't get to add anything to our N.
Cantor lies the foundation. Peano uses part of it which is always finite. Actually infinite is the dark rest.
>
> This is ironic, since the definition in you book
is Peano's potentially infinite collection.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-06-19 08:11 -0700 |
| Message-ID | <dd6a0fc3-9f12-4e6c-b838-68fb3dbc5441n@googlegroups.com> |
| In reply to | #602658 |
On Monday, June 19, 2023 at 9:15:46 AM UTC-4, Gus Gassmann wrote:
> On Monday, 19 June 2023 at 09:05:08 UTC-3, Timothy Golden wrote:
> [...]
> > Just as soon as the aleph comes up we have reached a new form of analysis.
> Not really.
> > We can only really toy with infinity... or at some level the seriousness of the work is diminished by the extreme results.
> No idea what this means. Let me just give you this example (due to Galileo):
> 1, 2, 3, 4, 5, ...
> 1, 4, 9, 16, 25, ...
>
> The first row are the natural numbers, the second row are their squares. It is clear that the second row omits some natural numbers (such as 2 and 3, 5, 6, 7, 8, etc.). So on the face of it, it seems that there should be more natural numbers than square.
>
> On the other hand, it should be equally clear that to every natural number corresponds its square, so there ought to be the *same* number of squares as there are natural numbers.
>
> This is not "toying", it is quite a deep dilemma, which is answered by set theory: There are two ways to determine the size of a set, through the subset relation (as in the first approach) and through the existence of a bijection (as in the second approach).
> > If only infinity had a maximum, but it is readily shown not to have such.
> This should be made more precise: There is no largest natural number.
> > Back to counting:
> > 1, 2, 3, ...
> > we admit this infinite sequence, but then interpretation takes off. Should we admit the Aleph we could write:
> > 1, 2, 3, ..., A
> > and when some mathematician complains about A+1, well, what then?
> Yes, what then? Mathematicians who accept set theory have no problem with that. (Look up "Ordinal numbers" on wikipedia, for instance.)
>
> Set theory distinguishes two types of numbers, ordinal numbers, "... a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite sets" (from the wikipedia article), and cardinal numbers, which measure the sizes of sets in the second sense of Galileo's conundrum. To distinguish ordinal and cardinal numbers, one uses the symbol ω (omega) for the smallest infinite ordinal and uses the Alephs (there is more than one) to measure the sizes of sets. The size of the set of natural numbers {1, 2, 3, ...} is \aleph_0, as is the size of the proper subset {1, 4, 9 16, 25, ...}. The size of the set of real numbers is *larger* than \aleph_0.
>
> The set of the natural numbers does not contain ω as an element, that is to say, ω is not a natural number.
>
> That's all.
> > And few trouble over the usage of the ellipsis; as if there is no problem there.
> Well, there isn't.
That is the standard position, yes. But the ellipses never halt.
Their connection to the infinite is obvious, and as you brush them off I just have to point out again, that the careful treatment should consider their meaning. It is the first usage of infinity without a care, right?
Working the digits as the speediest way to instantiate infinity do you brush off my usage of the ellipses? Seems you do.
What we both are getting is that there are many infinities. Some are definitely larger than others.
> > The halting problem is for others to worry about, right?
> The halting problem does not come into this. It is true that one cannot write down all the natural numbers, one by one, in a finite amount of time, so a Turing machine that counts 1, 2, 3, ... will never stop, but that is immaterial for the existence of the *SET* of natural numbers, and meaningful statement one can make about it. Fully respecting omega and aleph, in the digital form, which automatically puts itself head over heels beyond your slow series form, I see aleph at:
|999...99
and then omega at:
1|000...00
which is simply aleph plus one. You see, that the digital form allows such computation is why I'm focused on it. Your style does not allow for this.
As well, in that the ellipses signal an aleph of steps, let's say, then these digital forms are carrying aleph digits, and of course the highest of these in radix ten is going to be awfully large. The only way to get back down to your level is get down into radix one. This then exposes a contradiction in your own format: the usage of radix ten values for a radix one system is not satisfactory. Number theory has yet another quagmire there. If you thought that an infinite value could have a limited number of digits then you'd be mistaken. If you'd realize that the radix of those digits matters then you would not be mistaken.
[toc] | [prev] | [next] | [standalone]
| From | Gus Gassmann <horand.gassmann@gmail.com> |
|---|---|
| Date | 2023-06-19 08:20 -0700 |
| Message-ID | <1097db47-4709-4901-85dd-0953fdee3fc4n@googlegroups.com> |
| In reply to | #602684 |
On Monday, 19 June 2023 at 12:11:09 UTC-3, Timothy Golden wrote:
> On Monday, June 19, 2023 at 9:15:46 AM UTC-4, Gus Gassmann wrote:
> > On Monday, 19 June 2023 at 09:05:08 UTC-3, Timothy Golden wrote:
> > [...]
> > > Just as soon as the aleph comes up we have reached a new form of analysis.
> > Not really.
> > > We can only really toy with infinity... or at some level the seriousness of the work is diminished by the extreme results.
> > No idea what this means. Let me just give you this example (due to Galileo):
> > 1, 2, 3, 4, 5, ...
> > 1, 4, 9, 16, 25, ...
> >
> > The first row are the natural numbers, the second row are their squares. It is clear that the second row omits some natural numbers (such as 2 and 3, 5, 6, 7, 8, etc.). So on the face of it, it seems that there should be more natural numbers than square.
> >
> > On the other hand, it should be equally clear that to every natural number corresponds its square, so there ought to be the *same* number of squares as there are natural numbers.
> >
> > This is not "toying", it is quite a deep dilemma, which is answered by set theory: There are two ways to determine the size of a set, through the subset relation (as in the first approach) and through the existence of a bijection (as in the second approach).
> > > If only infinity had a maximum, but it is readily shown not to have such.
> > This should be made more precise: There is no largest natural number.
> > > Back to counting:
> > > 1, 2, 3, ...
> > > we admit this infinite sequence, but then interpretation takes off. Should we admit the Aleph we could write:
> > > 1, 2, 3, ..., A
> > > and when some mathematician complains about A+1, well, what then?
> > Yes, what then? Mathematicians who accept set theory have no problem with that. (Look up "Ordinal numbers" on wikipedia, for instance.)
> >
> > Set theory distinguishes two types of numbers, ordinal numbers, "... a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite sets" (from the wikipedia article), and cardinal numbers, which measure the sizes of sets in the second sense of Galileo's conundrum. To distinguish ordinal and cardinal numbers, one uses the symbol ω (omega) for the smallest infinite ordinal and uses the Alephs (there is more than one) to measure the sizes of sets. The size of the set of natural numbers {1, 2, 3, ...} is \aleph_0, as is the size of the proper subset {1, 4, 9 16, 25, ...}. The size of the set of real numbers is *larger* than \aleph_0.
> >
> > The set of the natural numbers does not contain ω as an element, that is to say, ω is not a natural number.
> >
> > That's all.
> > > And few trouble over the usage of the ellipsis; as if there is no problem there.
> > Well, there isn't.
> That is the standard position, yes. But the ellipses never halt.
In the set {1, 2, 3, ...} there is only one ellipsis. If you are referring to the *CLASS* of all ordinals, again, so what. If you wanted to use a computer to "count", you'd get stuck at the first ellipsis. True, but not relevant. There is no problem *reasoning about* further ellipses.
> Their connection to the infinite is obvious, and as you brush them off I just have to point out again, that the careful treatment should consider their meaning.
This is spelled out quite clearly in the wikipedia article. Did you read it?
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-19 06:18 -0700 |
| Message-ID | <adab2cdd-ebad-4d65-b683-dcf0b90abd0bn@googlegroups.com> |
| In reply to | #602610 |
Fritz Feldhase schrieb am Sonntag, 18. Juni 2023 um 18:40:44 UTC+2: > On Sunday, June 18, 2023 at 3:10:04 PM UTC+2, WM wrote: > > > D is defined as the least [real number x > 0 such that (0, x] is] containing ℵo unit fractions. > > Well, it's not possible to define such a D since there IS no "least real number x > 0 such that (0, x] is containing ℵo unit fractions", Then consider C, the minimum length occupied by 100 unit fractions. C is dark but existing, because never 100 unit fractions can sit at one point. > > Hint: For each and every D e IR, D > 0, there are infinitely many unit fractions in (0, D]. That is wrong. > > Note that there is no minimal x e IR, such that x > 0. (For each and every x: if x e IR, x > 0, then x/2 e IR, x/2 > 0 and x/2 < x.) But every distance between two unit fractions is larger than 0. Therefore ∀x ∈ (0, 1]: NUF(x) = ℵo is wrong because it assumes the limit 0 which provably cannot be taken. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-19 07:12 -0700 |
| Message-ID | <e86e312a-b341-48bd-94a4-e347d8f0e274n@googlegroups.com> |
| In reply to | #602659 |
On Monday, June 19, 2023 at 3:18:35 PM UTC+2, WM wrote: > Fritz Feldhase schrieb am Sonntag, 18. Juni 2023 um 18:40:44 UTC+2: > > On Sunday, June 18, 2023 at 3:10:04 PM UTC+2, WM wrote: > > > > > > D is defined as the least [real number x > 0 such that (0, x] is] containing ℵo unit fractions. > > > > > Well, it's not possible to define such a D since there IS no "least real number x > 0 such that (0, x] is containing ℵo unit fractions", > > > > Hint: For each and every D e IR, D > 0, there are infinitely many unit fractions in (0, D]. > > > That is wrong. No, that is NOT wrong, you psychotic asshole full of shit! Der Beweis dafür ist so trivial, dass selbst ein Volltrottel ihn (eigentlich) verstehen müsste. Das Intervall (0, 1] enthält UNENDLICH VIELE Einheitsbrüche. Für jedes D e IR, D > 0 gilt aber, dass (D, 1] nur ENDLICH VIELE Einheitsbrüche enthält; also müssen in (0, D] UNENDLICH VIELE Einheitsbrüche "übrig bleiben" (=enthalten sein). Wie dumm kann man eigenlich sein, Mückenheim? > Therefore > ∀x ∈ (0, 1]: NUF(x) = ℵo > is correct.
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-20 08:45 -0700 |
| Message-ID | <bb4ac1a4-9340-4d1c-8646-942d11f2bef2n@googlegroups.com> |
| In reply to | #602674 |
Fritz Feldhase schrieb am Montag, 19. Juni 2023 um 16:12:54 UTC+2: > On Monday, June 19, 2023 at 3:18:35 PM UTC+2, WM wrote: > > Therefore > > ∀x ∈ (0, 1]: NUF(x) = ℵo > > is > correct. Wrong. At least ℵo points of (0, 1] are mising. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-20 10:38 -0700 |
| Message-ID | <215a7a72-7d3d-45b6-b728-ead339d334b4n@googlegroups.com> |
| In reply to | #602783 |
On Tuesday, June 20, 2023 at 5:45:48 PM UTC+2, WM wrote: > Fritz Feldhase schrieb am Montag, 19. Juni 2023 um 16:12:54 UTC+2: > > On Monday, June 19, 2023 at 3:18:35 PM UTC+2, WM wrote: > > > > > > Therefore > > > ∀x ∈ (0, 1]: NUF(x) = ℵo > > > is > > > > > correct. > > > Wrong. No, (provable) correct.
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-20 14:39 -0700 |
| Message-ID | <d6c6f6d7-209a-4b2e-8382-cd49d9b60d36n@googlegroups.com> |
| In reply to | #602797 |
Fritz Feldhase schrieb am Dienstag, 20. Juni 2023 um 19:38:14 UTC+2: > On Tuesday, June 20, 2023 at 5:45:48 PM UTC+2, WM wrote: > > Fritz Feldhase schrieb am Montag, 19. Juni 2023 um 16:12:54 UTC+2: > > > On Monday, June 19, 2023 at 3:18:35 PM UTC+2, WM wrote: > > > > > > > > Therefore > > > > ∀x ∈ (0, 1]: NUF(x) = ℵo > > > > is > > > > > > > correct. > > > > > Wrong. > No, (provable) correct. Try to think until you have got it: There are at least 100 points x in (0, 1] with NUF(x) < 100. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-18 06:04 -0700 |
| Message-ID | <e41a1eb8-94dc-4664-9ba0-3d38bec339afn@googlegroups.com> |
| In reply to | #602538 |
Fritz Feldhase schrieb am Samstag, 17. Juni 2023 um 19:10:03 UTC+2: > On Saturday, June 17, 2023 at 3:26:39 PM UTC+2, WM wrote: > > You cannot compress 10 unit fractions into a point. > Did anyone claim that this nonsense is or may be possible It was claimed: ∀x ∈ (0, 1]: NUF(x) = ℵo which is wrong because ∀x ∈ (0, 1]: NUF(x) > 100 is wrong. > > What does it even mean? The minimum interval C containing 100 unit fractions is larger than 0. Therefore ∀x ∈ (C, 1]: NUF(x) > 100. Regards WM
[toc] | [prev] | [next] | [standalone]
| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-06-19 09:34 -0400 |
| Message-ID | <9d8c3ce7-eb70-5b33-b44f-e07fb394af30@att.net> |
| In reply to | #602594 |
On 6/18/2023 9:04 AM, WM wrote: > Fritz Feldhase schrieb am Samstag, > 17. Juni 2023 um 19:10:03 UTC+2: [...] > ∀x ∈ (0, 1]: NUF(x) > 100 > is wrong. No. ∀x ∈ (0, 1]: NUF(x) > 100 is correct. Each x ∈ (0,1] is preceded by a unit fraction. ∀x ∈ (0, 1]: ∃mₓ ∈ ℕ⁺: ⅟x < mₓ ≤ 1+⅟x ⅟mₓ ∈ (0,x)∩⅟ℕ⁺ Each x ∈ (0, 1] is preceded by 101 unit fractions. ∀x ∈ (0, 1]: ( ∃mₓ ∈ ℕ⁺: ⅟x < mₓ ≤ 1+⅟x ⅟mₓ e (0,x)∩⅟ℕ⁺ |(⅟(mₓ+100), ⅟mₓ)∩⅟ℕ⁺| = 101 (⅟(mₓ+100), ⅟mₓ)∩⅟ℕ⁺ ⊆ (0,x]∩⅟ℕ⁺ ) |(0,x]∩⅟ℕ⁺| > 100 ∀x ∈ (0, 1]: |(0,x]∩⅟ℕ⁺| > 100 NUF(x) > 100 ∀x ∈ (0, 1]: ∃m ∈ ℕ⁺: ⅟x < m ≤ 1+⅟x ¬∃m ∈ ℕ⁺: ∀x ∈ (0, 1]: ⅟x < m ≤ 1+⅟x | Assume otherwise. | Assume | ∀x ∈ (0, 1]: | ⅟x < mᣔ ≤ 1+⅟x | ⅟mᣔ ≤ x < ⅟(mᣔ-1) | | Let xₘ := ⅟(mᣔ+1) | ¬(⅟mᣔ ≤ xₘ < ⅟(mᣔ-1)) | Contradiction. That does not contradict ∀x ∈ (0, 1]: NUF(x) > 100
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-20 08:44 -0700 |
| Message-ID | <b52f5a0e-3ea5-4f72-83e2-a1d9d4facd92n@googlegroups.com> |
| In reply to | #602661 |
Jim Burns schrieb am Montag, 19. Juni 2023 um 15:34:13 UTC+2: > On 6/18/2023 9:04 AM, WM wrote: > > ∀x ∈ (0, 1]: NUF(x) > 100 > > is wrong. > No. > ∀x ∈ (0, 1]: NUF(x) > 100 > is correct. Wrong. At least 100 points in (0, 1] are missing. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-06-20 13:31 -0400 |
| Message-ID | <e7915ec7-d3a0-82d8-86d4-ee90b7ca9421@att.net> |
| In reply to | #602782 |
On 6/20/2023 11:44 AM, WM wrote: > Jim Burns schrieb am Montag, > 19. Juni 2023 um 15:34:13 UTC+2: >> On 6/18/2023 9:04 AM, WM wrote: >>> ∀x ∈ (0, 1]: NUF(x) > 100 >>> is wrong. >> >> No. >> ∀x ∈ (0, 1]: NUF(x) > 100 >> is correct. > > Wrong. > At least 100 points in (0, 1] are missing. More than 100 different, not-missing points are in (0,x] For each m,n ∈ ℕ⁺ there is a sequence of unit fractions [⅟(m+n),⅟m] ∩ ⅟ℕ⁺ from ⅟(m+n) to ⅟m which holds n+1 unit fractions. n+1 > n | | ∀m ∈ ℕ⁺: | ∀n ∈ ℕ⁺: | |[⅟(m+n),⅟m] ∩ ⅟ℕ⁺| = n+1 > n For each x ∈ (0,1] unit fraction ⅟mₓ exists before x | | ∀x ∈ (0,1]: | ∃mₓ ∈ ℕ⁺: | ⅟x ≤ mₓ < 1+⅟x | 0 < ⅟mₓ ≤ x | ⅟mₓ ∈ (0,x]∩⅟ℕ⁺ For each x ∈ (0,1] mₓ exists before x such that, for each n ∈ ℕ⁺ ⅟(mₓ+n) is a unit fraction before x | | ∀x ∈ (0,1]: | ∃mₓ ∈ ℕ⁺: | ∀n ∈ ℕ⁺: | ⅟x ≤ mₓ+n | 0 < ⅟(mₓ+n) ≤ x | ⅟(mₓ+n) ∈ (0,x]∩⅟ℕ⁺ For each x ∈ (0,1] mₓ exists such that, for each n ∈ ℕ⁺ a sequence of unit fractions from ⅟(mₓ+n) to ⅟mₓ before x exists and has more than n unit fractions. There are more than n unit fractions before x. | | ∀x ∈ (0,1]: | ∃mₓ ∈ ℕ⁺: | ∀n ∈ ℕ⁺: | ([⅟(mₓ+n),1/mₓ] ∩ ⅟ℕ⁺) ⊆ (0,x]∩⅟ℕ⁺ | |[⅟(mₓ+n),1/mₓ] ∩ ⅟ℕ⁺| = n+1 > n | |(0,x]∩⅟ℕ⁺| > n | NUF(x) > n 👁¬#1◇⊥ (valid) swap ∃∀⇒∀∃ For each x ∈ (0,1] for each n ∈ ℕ⁺ mₓ exists such that, a sequence of unit fractions from ⅟(mₓ+n) to ⅟mₓ before x exists and has more than n unit fractions. There are more than n unit fractions before x. | | ∀x ∈ (0,1]: | ∀n ∈ ℕ⁺: | ( ∃mₓ ∈ ℕ⁺: | ([⅟(mₓ+n),1/mₓ] ∩ ⅟ℕ⁺) ⊆ (0,x]∩⅟ℕ⁺ | |[⅟(mₓ+n),1/mₓ] ∩ ⅟ℕ⁺| = n+1 > n ) | |(0,x]∩⅟ℕ⁺| > n | NUF(x) > n For each x ∈ (0,1] for each n ∈ ℕ⁺ there are more than n unit fractions before x. | | ∀x ∈ (0,1]: | ∀n ∈ ℕ⁺: | |(0,x]∩⅟ℕ⁺| > n | NUF(x) > n In particular, for each x ∈ (0,1] there are more than 100 unit fractions before x. | | ∀x ∈ (0,1]: | |(0,x]∩⅟ℕ⁺| > 100 | NUF(x) > 100 And, more generally, for each x ∈ (0,1] the unit fractions before x aren't finitely-many. | | ∀x ∈ (0,1]: | |(0,x]∩⅟ℕ⁺| ∉ ℕ | NUF(x) ∉ ℕ
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-20 14:37 -0700 |
| Message-ID | <eb287635-11d4-4814-9248-9361614a4de6n@googlegroups.com> |
| In reply to | #602796 |
Jim Burns schrieb am Dienstag, 20. Juni 2023 um 19:31:22 UTC+2: > On 6/20/2023 11:44 AM, WM wrote: > > Jim Burns schrieb am Montag, > > 19. Juni 2023 um 15:34:13 UTC+2: > >> On 6/18/2023 9:04 AM, WM wrote: > > >>> ∀x ∈ (0, 1]: NUF(x) > 100 > >>> is wrong. > >> > >> No. > >> ∀x ∈ (0, 1]: NUF(x) > 100 > >> is correct. > > > > Wrong. > > At least 100 points in (0, 1] are missing. > More than 100 different, not-missing points > are in (0,x] Nevertheless there are at least 100 points x in (0, 1] with NUF(x) < 100 Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-20 15:03 -0700 |
| Message-ID | <a446007b-b41a-4ba8-bb2a-da11fda75694n@googlegroups.com> |
| In reply to | #602833 |
On Tuesday, June 20, 2023 at 11:37:23 PM UTC+2, WM wrote: > there are at least 100 points x in (0, 1] with NUF(x) < 100 Nein, Du psychotischer Spinner, there is *no* x in with NUF(x) < 100. Halt doch einfach mal die Fresse, Mann. Oder gehe endlich mal zum Psychiater!
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-20 15:05 -0700 |
| Message-ID | <fc008760-e13f-4b1d-a945-1f605dd8da2bn@googlegroups.com> |
| In reply to | #602839 |
On Wednesday, June 21, 2023 at 12:03:57 AM UTC+2, Fritz Feldhase wrote: > On Tuesday, June 20, 2023 at 11:37:23 PM UTC+2, WM wrote: > > > > there are at least 100 points x in (0, 1] with NUF(x) < 100 > > > Nein, Du psychotischer Spinner, there is *no* x in with NUF(x) < 100. Hinweis: Für jedes x ∈ (0, 1] sind die die Zahlen 1/ceil(1/x), 1/(ceil(1/x) + 1), ..., 1/(ceil(1/x) + 100) kleiner-gleich x. Und das sind MEHR als 100 Stammbrüche, Du hirnloser Affe. > Halt doch einfach mal die Fresse, Mann. > > Oder gehe endlich mal zum Psychiater!
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-21 06:53 -0700 |
| Message-ID | <f29341e1-c81b-46c5-9b00-4a96a76c1864n@googlegroups.com> |
| In reply to | #602840 |
Fritz Feldhase schrieb am Mittwoch, 21. Juni 2023 um 00:06:01 UTC+2: > On Wednesday, June 21, 2023 at 12:03:57 AM UTC+2, Fritz Feldhase wrote: > > On Tuesday, June 20, 2023 at 11:37:23 PM UTC+2, WM wrote: > > > > > > there are at least 100 points x in (0, 1] with NUF(x) < 100 > > > > > Nein, Du psychotischer Spinner, there is *no* x in with NUF(x) < 100. > Hinweis: Für jedes x ∈ (0, 1] das Du wählen kannst > sind die die Zahlen 1/ceil(1/x), 1/(ceil(1/x) + 1), ..., 1/(ceil(1/x) + 100) kleiner-gleich x. Und das sind MEHR als 100 Stammbrüche, Die passen aber nicht zwischen 0 und jedes x, denn dazwischen passt gar nichts, nichzt einmal ein Stammbruch und erst recht nicht zwei. Gruß, WM
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-21 06:50 -0700 |
| Message-ID | <c0ec2174-12e5-4e3f-a72a-b6786b2dabd4n@googlegroups.com> |
| In reply to | #602839 |
Fritz Feldhase schrieb am Mittwoch, 21. Juni 2023 um 00:03:57 UTC+2: > On Tuesday, June 20, 2023 at 11:37:23 PM UTC+2, WM wrote: > > > there are at least 100 points x in (0, 1] with NUF(x) < 100 > there is *no* x in with NUF(x) < 100. Then the points are not fixed but moving and appearing, depending on what you have considered previously. I do not accept that. The points are fixed and for exery x there is a clear answer to the question is NUF(x) = 0, is NUF(x) = 1, and so on, NUF(x) < 100 or NUF(x) ≥ 100? But we can't know points with less than NUF(x) = ℵo. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-21 07:37 -0700 |
| Message-ID | <8e4737a9-c144-4c78-82d4-b7bdfd9beba8n@googlegroups.com> |
| In reply to | #602885 |
On Wednesday, June 21, 2023 at 3:51:02 PM UTC+2, WM wrote: > > for exery x [ in (0, 1] ] there is a clear answer to the question is NUF(x) = 0, is NUF(x) = 1, and so on, Indeed! And the answer is in all cases is "no". Hint: Ax e (0, 1]: An e IN: NUF(x) =/= n. > NUF(x) < 100 or NUF(x) ≥ 100? NUF(x) ≥ 100 natürlich. Den trivialen Beweis dafür habe ich hier doch schon gepostet, Du psychotischer Spinner! Für jedes x ∈ (0, 1] sind die die Zahlen 1/ceil(1/x), 1/(ceil(1/x) + 1), ..., 1/(ceil(1/x) + 100) kleiner-gleich x. Und das sind MEHR als 100 Stammbrüche. > [...] > > [Hence] we can't know points [ x in (0, 1] ] with NUF(x) < ℵo. Natürlich nicht, da man ja etwas, das es nicht gibt, (prinzipiell) nicht "kennen" kann (jedenfalls nicht persönlich).
[toc] | [prev] | [next] | [standalone]
Page 6 of 9 — ← Prev page 1 2 3 4 5 [6] 7 8 9 Next page →
Back to top | Article view | sci.math
csiph-web