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 7 of 9 — ← Prev page 1 2 3 4 5 6 [7] 8 9 Next page →
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-22 06:13 -0700 |
| Message-ID | <f5d5e0a9-ca92-45b9-96dd-793ccd5589d4n@googlegroups.com> |
| In reply to | #602890 |
Fritz Feldhase schrieb am Mittwoch, 21. Juni 2023 um 16:37:05 UTC+2: > > 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). For NUF(x) > 100 there must be at least 100 real positive points at the left-hand side of x. This cannot be true for all positive x because there remain no positive points between 0 and (0, 1] = all positive points between 0 and 1. If you claim ℵo unit fraction between every x and 0 also for x which have no positive points between themselves and 0, then you are wrong. You can claim this sensibly only for x which have ℵo positive points between them selves and 0. But you try to claim it for all points, namely the interval (0, 1]. You should distinguish between all points that you can define and all points which can be taken only collectively but completely such that none remains. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-06-20 20:34 -0400 |
| Message-ID | <b77b6092-fa02-879f-1884-e97b2ed524fc@att.net> |
| In reply to | #602833 |
On 6/20/2023 5:37 PM, WM wrote: > 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 No. for each x ∈ (0,1] last ⅟mₓ₁ in (0,x) exists ⅟x < mₓ₁ ≤ 1+⅟x last ⅟mₓ₂ in (0,⅟mₓ₁) exists mₓ₂ = mₓ₁+1 last ⅟mₓ₃ in (0,⅟mₓ₂) exists mₓ₃ = mₓ₂+1 ... last ⅟mₓ₁₀₁ in (0,⅟mₓ₁₀₀) exists mₓ₁₀₁ = mₓ₁₀₀+1 for each x ∈ (0,1] ⟨⅟mₓ₁₀₁…⅟mₓ₁⟩ ⊆ (0,x] NUF(x) > 100
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-21 06:59 -0700 |
| Message-ID | <50163bd8-9180-47fe-b668-b06fe02a43f6n@googlegroups.com> |
| In reply to | #602850 |
Jim Burns schrieb am Mittwoch, 21. Juni 2023 um 02:34:58 UTC+2: > On 6/20/2023 5:37 PM, WM wrote: > > Nevertheless there are > > at least 100 points x in (0, 1] > > with NUF(x) < 100 > No. 100 unit fractions don't fit between 0 and (0, 1]. > > for each x ∈ (0,1] that can be defined > last ⅟mₓ₁ in (0,x) exists Let's talk about the interval (0, 1]. No unit fraction fits between it and zero. Hope you will agree. Together with your above claim that means you cannot define every x of that interval. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-06-21 11:58 -0400 |
| Message-ID | <ae78fbf2-a493-dfda-d1b0-32c0a14626e4@att.net> |
| In reply to | #602887 |
On 6/21/2023 9:59 AM, WM wrote: > Jim Burns schrieb am Mittwoch, > 21. Juni 2023 um 02:34:58 UTC+2: >> On 6/20/2023 5:37 PM, WM wrote: >>> Nevertheless there are >>> at least 100 points x in (0, 1] >>> with NUF(x) < 100 >> >> No. > > 100 unit fractions don't fit > between 0 and (0, 1]. It is true about x ∈ (0,1] that more than 100 unit fractions are between 0 and x We know that without knowing _which_ x ∈ (0,1] is referred to. >> for each x ∈ (0,1] > > that can be defined No. Which exists. 0 exists. ⟨x,y⟩ exists if x, y exist. j⁺⁺ := ⟨j,0⟩ exists if j exists ⟨0…j,j⁺⁺⟩ exists if ⟨0…j⟩ exists j ∈ ℕ exists if ⟨0…j⟩ exists k ∈ ℤ: k = a-b exists if a,b ∈ ℕ exist r ∈ ℚ: r = p/q exists if q≠0 and p,q ∈ ℤ exist u ∈ 1/ℕ⁺: u = 1/n exists if n ∈ ℕ⁺ exists for each x ∈ (0,1] ⟨⅟mₓ₁₀₁…⅟mₓ₁⟩ ⊆ (0,x] NUF(x) := |(0,x]∩⅟ℕ⁺| NUF(x) > 100 True for definables which exist and true for undefinables (if any) which exist. >> last ⅟mₓ₁ in (0,x) exists > > Let's talk about the interval (0, 1]. > No unit fraction fits between it and zero. That does not have the consequences to which you feel entitled. for each x ∈ (0,1] ⟨⅟mₓ₁₀₁…⅟mₓ₁⟩ ⊆ (0,x] NUF(x) := |(0,x]∩⅟ℕ⁺| NUF(x) > 100
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-22 06:19 -0700 |
| Message-ID | <a511f12e-bd87-451e-8ccd-556f2b1aae43n@googlegroups.com> |
| In reply to | #602897 |
Jim Burns schrieb am Mittwoch, 21. Juni 2023 um 17:59:07 UTC+2: > On 6/21/2023 9:59 AM, WM wrote: > > Jim Burns schrieb am Mittwoch, > > 21. Juni 2023 um 02:34:58 UTC+2: > >> On 6/20/2023 5:37 PM, WM wrote: > > >>> Nevertheless there are > >>> at least 100 points x in (0, 1] > >>> with NUF(x) < 100 > >> > >> No. > > > > 100 unit fractions don't fit > > between 0 and (0, 1]. > It is true about x ∈ (0,1] > that > more than 100 unit fractions are > between 0 and x It is true for every definable x. It is not true for all x, i.e., the whole interval. > > We know that without knowing > _which_ x ∈ (0,1] is referred to. We know that for NUF(x) >= 100 there must be at least 100 real positive points at the left-hand side of x. This cannot be true for all positive x because there remain no positive points between 0 and (0, 1]. Regards, WM > > Let's talk about the interval (0, 1]. > > No unit fraction fits between it and zero. > That does not have the consequences It has the consequence that no unit fraction fits berween every x and zero. > NUF(x) > 100 Not for an x with less than 100 points between itself and 0. Such x can only be treated collectively. But if they would not exist, then the interval (0, 1] would not exist complete enough to know that between 0 and (0, 1] nothing fits. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2023-06-22 12:30 -0400 |
| Message-ID | <f700264e-a44d-c52d-d5c7-6cf1526835d3@att.net> |
| In reply to | #602955 |
On 6/22/2023 9:19 AM, WM wrote: > Jim Burns schrieb am Mittwoch, > 21. Juni 2023 um 17:59:07 UTC+2: >> On 6/21/2023 9:59 AM, WM wrote: >>> Let's talk about the interval (0, 1]. >>> No unit fraction fits between it and zero. >> >> That does not have the consequences > > It has the consequence that > no unit fraction fits > berween every x and zero. That does not have the consequences to which you feel entitled. A unit fraction ⅟mₓ₁ exists between that x and 0 ⅟x < mₓ₁ =< 1+⅟x : 0 < ⅟mₓ₁ < x Also existing mₓ₂ = mₓ₁+1 : 0 < ⅟mₓ₂ < ⅟mₓ₁ mₓ₃ = mₓ₂+1 : 0 < ⅟mₓ₃ < ⅟mₓ₂ mₓ₄ = mₓ₃+1 : 0 < ⅟mₓ₄ < ⅟mₓ₃ ... mₓ₁₀₁ = mₓ₁₀₀+1 : 0 < ⅟mₓ₁₀₁ < ⅟mₓ₁₀₀ >> NUF(x) > 100 > > Not for an x with less than 100 points > between itself and 0. No. 0 < ⅟mₓ₁₀₁ < ... < ⅟mₓ₁ < x > Such x can only be treated collectively. Collectively, what you describe not-exists. Not "exists darkly", _not-exists_ > But if they would not exist, > then the interval (0, 1] would not > exist complete enough to know that > between 0 and (0, 1] nothing fits. No. We know nothing fits between 0 and (0,1] and we know 0 < NUF(x) < 101 not-exists. Nothing fits between 0 and (0,1] ¬∃x ∈ ℝ: 0 < x <ᣔ (0,1] | Assume otherwise. | Assume | 0 < xₓ <ᣔ (0,1] | ∀y ∈ (0,1]]: | 0 < xₓ < y ≤ 1 | | However, | let yₓₓ := xₓ | ¬( 0 < xₓ < yₓₓ ≤ 1 ) | Contradiction. And also 0 < ⅟mₓ₁₀₁ < ... < ⅟mₓ₁ < x
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-22 10:38 -0700 |
| Message-ID | <243a7a34-2457-400f-8ca8-4918d89d9c93n@googlegroups.com> |
| In reply to | #602959 |
On Thursday, June 22, 2023 at 6:30:22 PM UTC+2, Jim Burns wrote: > Nothing fits between 0 and (0,1] > ¬∃x ∈ ℝ: 0 < x <ᣔ (0,1] Good idea to denote this "order-realation" "between a number and an interval/a set of numbers" with <^, or something like that. x <^ I :<-> Ay e I: x < I (where I c IR). I guess, we might even be able to do without that (by the usual abuse of notation), but in the context of a crank/Mückenheim thread this might be a rather bad idea. ___________________________________________ Btw. Mückenheim's "argument" relies on his usual "quantifier shift" (at least if viewed superficially). Actually, it's even worse: _For him_ imho "Ey Ax e (0,1] ..." does not differ "in meaning" from "Ax e (0,1] Ey ..." In other words, it seems to me that his "mental representation" of "Ey Ax e (0,1] ..." is identical with his "mental representation" of "Ax e (0,1] Ey ...". So at a deeper level of (his) "thinking" he does not even perfom an inavlid "quantifier shift" ... That's why he seems COMPLETELY ignorant of that point, even after all these years.
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-22 20:18 -0700 |
| Message-ID | <455d3725-4b36-489f-9c45-c660076c6defn@googlegroups.com> |
| In reply to | #602962 |
On Thursday, June 22, 2023 at 7:38:26 PM UTC+2, Fritz Feldhase wrote: Correction: > x <^ I :<-> Ay e I: x < I (where I c IR). ==> x <^ I :<-> Ay e I: x < y (where I c IR).
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-23 10:06 -0700 |
| Message-ID | <5070c0a0-f84e-4a4a-883b-8f4a8e38aa6dn@googlegroups.com> |
| In reply to | #602962 |
Fritz Feldhase schrieb am Donnerstag, 22. Juni 2023 um 19:38:26 UTC+2: > Btw. Mückenheim's "argument" relies on his usual "quantifier shift" (at least if viewed superficially). No, if there is no x with NUF(x) < ℵ₀, then for all x in (0, 1] NUF(x) = ℵ₀ which is wrong for at least ℵ₀ points x in (0, 1], because ℵ₀ unit fractions occupy ℵ₀ points of (0, 1]. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-23 10:17 -0700 |
| Message-ID | <daeac966-7355-4c12-9cf1-a6101d431e21n@googlegroups.com> |
| In reply to | #603042 |
On Friday, June 23, 2023 at 7:06:29 PM UTC+2, WM wrote: > NUF(x) = ℵ₀ [...] is wrong for at least ℵ₀ points x in (0, 1] Nope. It's not even wrong for a single x in (0, 1]. In other words, the following holds: for all x in (0, 1]: NUF(x) = ℵ₀. > because ℵ₀ unit fractions occupy ℵ₀ points of (0, 1]. Huh?!
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-23 10:24 -0700 |
| Message-ID | <3a9b30c4-03a0-4d51-9f0a-c99f1be9cf76n@googlegroups.com> |
| In reply to | #603048 |
Fritz Feldhase schrieb am Freitag, 23. Juni 2023 um 19:17:33 UTC+2: > On Friday, June 23, 2023 at 7:06:29 PM UTC+2, WM wrote: > > > NUF(x) = ℵ₀ [...] is wrong for at least ℵ₀ points x in (0, 1] > > Nope. It's not even wrong for a single x in (0, 1]. > > In other words, the following holds: for all x in (0, 1]: NUF(x) = ℵ₀. Thank you, I will tell my students your opinion. They shall decide. I will inform you. Further discussing it is not useful. Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-15 06:16 -0700 |
| Message-ID | <2cb3faa3-f304-4be7-9695-17a1a806741bn@googlegroups.com> |
| In reply to | #602234 |
Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
Correction:
> I.e. that there are "more" functions from N to {0,1} than there are
> natural numbers.
Of course. But there are more different terms of the sequences than sequences.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Gus Gassmann <horand.gassmann@gmail.com> |
|---|---|
| Date | 2023-06-15 09:50 -0700 |
| Message-ID | <ffe88150-6487-4373-b915-5ac614c084d7n@googlegroups.com> |
| In reply to | #602316 |
On Thursday, 15 June 2023 at 10:17:03 UTC-3, WM wrote:
> Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
>
> Correction:
> > I.e. that there are "more" functions from N to {0,1} than there are
> > natural numbers.
> Of course. But there are more different terms of the sequences than sequences.
Your usual double speak. Learn proper use of quantifiers. Ah, wait: "You are just too stupid."
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-15 14:00 -0700 |
| Message-ID | <a4fc1354-8170-4bbf-b8fe-f29d153d475en@googlegroups.com> |
| In reply to | #602344 |
Gus Gassmann schrieb am Donnerstag, 15. Juni 2023 um 18:50:27 UTC+2:
> On Thursday, 15 June 2023 at 10:17:03 UTC-3, WM wrote:
> > Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
> >
> > Correction:
> > > I.e. that there are "more" functions from N to {0,1} than there are
> > > natural numbers.
> > Of course. But there are more different terms of the sequences than sequences.
> Your usual double speak.
No. For levels 0 to n we have 2^n complete paths but 2^(n+1) -1 nodes. What miracle should change this ratio "in the infinite"? Neither nodes nor paths exist in the infinite.
A miracle is that so many mathematicians are stupid enough to believe this inane hocupocus.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-16 01:28 +0100 |
| Message-ID | <87zg50ntc6.fsf@bsb.me.uk> |
| In reply to | #602316 |
WM <askasker48@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)
> Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
>
> Correction:
>
>> I.e. that there are "more" functions from N to {0,1} than there are
>> natural numbers.
>
> Of course. But there are more different terms of the sequences than
> sequences.
There are only two different terms: 0 and 1.
--
Ben.
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-16 07:50 -0700 |
| Message-ID | <ecba25d6-e02f-44d2-8439-98a966129102n@googlegroups.com> |
| In reply to | #602398 |
Ben Bacarisse schrieb am Freitag, 16. Juni 2023 um 02:28:51 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 Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
> >
> > Correction:
> >
> >> I.e. that there are "more" functions from N to {0,1} than there are
> >> natural numbers.
> >
> > Of course. But there are more different terms of the sequences than
> > sequences.
> There are only two different terms: 0 and 1.
No, there are many. Each term (node) is a triple of level number, index within the level, and value 0 or 1. My claim is that there are more nodes than paths up to each level, which is undisputed. A reversal of the ratio is unreasonable belief.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-18 02:13 +0100 |
| Message-ID | <87pm5tmv2l.fsf@bsb.me.uk> |
| In reply to | #602451 |
WM <askasker48@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)
> Ben Bacarisse schrieb am Freitag, 16. Juni 2023 um 02:28:51 UTC+2:
>> WM <askas...@gmail.com> writes:
>> > Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
>> >
>> > Correction:
>> >
>> >> I.e. that there are "more" functions from N to {0,1} than there are
>> >> natural numbers.
>> >
>> > Of course. But there are more different terms of the sequences than
>> > sequences.
>> There are only two different terms: 0 and 1.
>
> No, there are many.
No. You were talking, it seems, about what I wrote. If you don't
understand what I wrote, ask for an explanation or don't reply. The
functions from N to {0,1} are sequences with only two different terms.
--
Ben.
[toc] | [prev] | [next] | [standalone]
| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-18 06:19 -0700 |
| Message-ID | <ed0b9b85-6e17-4a64-b3e5-5e154237bb8en@googlegroups.com> |
| In reply to | #602568 |
Ben Bacarisse schrieb am Sonntag, 18. Juni 2023 um 03:13:33 UTC+2:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Technische Hochschule Augsburg.)
>
> > Ben Bacarisse schrieb am Freitag, 16. Juni 2023 um 02:28:51 UTC+2:
> >> WM <askas...@gmail.com> writes:
> >> > Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
> >> >
> >> > Correction:
> >> >
> >> >> I.e. that there are "more" functions from N to {0,1} than there are
> >> >> natural numbers.
> >> >
> >> > Of course. But there are more different terms of the sequences than
> >> > sequences.
> >> There are only two different terms: 0 and 1.
> >
> > No, there are many.
> No. You were talking, it seems, about what I wrote.
No, I ws talking about true mathematics. There every node of the Binary Tree is defined by a triple of numbers. The number of these nodes surpasses the number of paths.
> If you don't understand what I wrote, ask for an explanation or don't reply.
I reply only because you don't understad what you wrote.
> The
> functions from N to {0,1} are sequences with only two different terms.
Nonsense. The function 0, 0, 0, ... for instance, has infinitely many terms. Note the difference with sets where elements are different.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-20 01:26 +0100 |
| Message-ID | <87v8fjhtbo.fsf@bsb.me.uk> |
| In reply to | #602596 |
WM <askasker48@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)
> Ben Bacarisse schrieb am Sonntag, 18. Juni 2023 um 03:13:33 UTC+2:
>> WM <askas...@gmail.com> writes:
>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
>> Unendlichen" at Technische Hochschule Augsburg.)
You are again dishonestly editing quotes without noting the fact. Did
you not get any training in research ethics? By all means correct
things that are wrong, but don't misrepresent what people write.
>> > Ben Bacarisse schrieb am Freitag, 16. Juni 2023 um 02:28:51 UTC+2:
>> >> WM <askas...@gmail.com> writes:
>> >> > Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
>> >> >
>> >> > Correction:
>> >> >
>> >> >> I.e. that there are "more" functions from N to {0,1} than there are
>> >> >> natural numbers.
>> >> >
>> >> > Of course. But there are more different terms of the sequences than
>> >> > sequences.
>> >> There are only two different terms: 0 and 1.
>> >
>> > No, there are many.
>> No. You were talking, it seems, about what I wrote.
>
> No, I ws talking about true mathematics. There every node of the
> Binary Tree is defined by a triple of numbers. The number of these
> nodes surpasses the number of paths.
Then you should have made it clear you where not talking about the
remark you quoted. In fact you should not quote it if you are not going
to address it.
You know perfectly well that (infinite) sequences are functions of N.
It's even in your textbook so I know you know. I must interpret your
"there are more different terms of the sequences than sequences" as
referring to the sequences I wrote about, since you commented directly on
those sequences, not the ones you had in your head.
The functions from N to {0,1} are sequences of 0s and 1s, and they all
have only two different terms.
>> If you don't understand what I wrote, ask for an explanation or don't reply.
>
> I reply only because you don't understad what you wrote.
>
>> The
>> functions from N to {0,1} are sequences with only two different terms.
>
> Nonsense. The function 0, 0, 0, ... for instance, has infinitely many
> terms.
You must be being deliberately obtuse. There are infinitely many terms,
but only two different terms.
You hate talking about paths as functions from N to {0,1} because your
waffle about paths being "distinguished by nodes" is made to look a
foolish as it really is. Infinitely many such functions (i.e. paths) can
be distinguished despite there being only two different terms.
--
Ben.
[toc] | [prev] | [next] | [standalone]
| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-06-20 07:09 -0700 |
| Message-ID | <8a722f44-422a-4d80-b681-45b0950fc724n@googlegroups.com> |
| In reply to | #602750 |
On Monday, June 19, 2023 at 8:27:02 PM UTC-4, Ben Bacarisse wrote:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
> > Ben Bacarisse schrieb am Sonntag, 18. Juni 2023 um 03:13:33 UTC+2:
> >> WM <askas...@gmail.com> writes:
> >> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> >> Unendlichen" at Technische Hochschule Augsburg.)
> You are again dishonestly editing quotes without noting the fact. Did
> you not get any training in research ethics? By all means correct
> things that are wrong, but don't misrepresent what people write.
> >> > Ben Bacarisse schrieb am Freitag, 16. Juni 2023 um 02:28:51 UTC+2:
> >> >> WM <askas...@gmail.com> writes:
> >> >> > Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
> >> >> >
> >> >> > Correction:
> >> >> >
> >> >> >> I.e. that there are "more" functions from N to {0,1} than there are
> >> >> >> natural numbers.
> >> >> >
> >> >> > Of course. But there are more different terms of the sequences than
> >> >> > sequences.
> >> >> There are only two different terms: 0 and 1.
> >> >
> >> > No, there are many.
> >> No. You were talking, it seems, about what I wrote.
> >
> > No, I ws talking about true mathematics. There every node of the
> > Binary Tree is defined by a triple of numbers. The number of these
> > nodes surpasses the number of paths.
> Then you should have made it clear you where not talking about the
> remark you quoted. In fact you should not quote it if you are not going
> to address it.
>
> You know perfectly well that (infinite) sequences are functions of N.
> It's even in your textbook so I know you know. I must interpret your
> "there are more different terms of the sequences than sequences" as
> referring to the sequences I wrote about, since you commented directly on
> those sequences, not the ones you had in your head.
> mathematics
> The functions from N to {0,1} are sequences of 0s and 1s, and they all
> have only two different terms.
> >> If you don't understand what I wrote, ask for an explanation or don't reply.
> >
> > I reply only because you don't understad what you wrote.
> >
> >> The
> >> functions from N to {0,1} are sequences with only two different terms.
> >
> > Nonsense. The function 0, 0, 0, ... for instance, has infinitely many
> > terms.
> You must be being deliberately obtuse. There are infinitely many terms,
> but only two different terms.
>
> You hate talking about paths as functions from N to {0,1} because your
> waffle about paths being "distinguished by nodes" is made to look a
> foolish as it really is. Infinitely many such functions (i.e. paths) can
> be distinguished despite there being only two different terms.
>
> --
> Ben.
The best way to yield dark numbers is to pay attention to the radix.
The natural numbers, being a radix one concept, plod along so slowly toward infinity as they can merely find their successor in their digital makeup:
s( s( s( ...s( 1 ) ) ) ... )
This value is simply:
111...11
in radix one. We can call this then a representation of infinity; aleph if you like. However, entertaining higher radix systems, and technically we can still respect this aleph concept as now implied by the naturals except that it applies to the quantity of digits of the value, and for instance in our conventional radix-ten representation then, respecting this aleph, we can have:
999...99
whose infinite qualities are far more monstrous than the lowly naturals achieved. We can even increment this radix ten aleph and get omega:
1|000...00
and so computable forms of infinity arrive when we allow the tail of the digits, and lets face it: nobody ever built a computable value without a tail. In this regard ordinary mathematics gets it wrong when they write:
1/3 = 0.333...
and the correct representation should have been:
1/3 = 0.333...33
which is computable. The aptness of the radix point versus the aleph point can be expounded upon. Their distinction is minimal. Upon taking products double radix points and double aleph points will be exposed. As to the grotesqueness of those value... yet they can be incremented too.
The gains of this method are obvious. Why Cantor didn't do it I cannot say. It's simple enough really. The unreachable problems are still unreachable; it's not as if your new differential 0.000...01 is going to count up to unity, but you see it is its own unital form much like dimensional analysis.
Perhaps there is a carry into bra-ket notation: the product as a finite result can be had between a rank one aleph form and a rank one differential form. I think this is simpler, but maybe symmetrical other than the scale.
[toc] | [prev] | [next] | [standalone]
Page 7 of 9 — ← Prev page 1 2 3 4 5 6 [7] 8 9 Next page →
Back to top | Article view | sci.math
csiph-web