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Groups > comp.lang.c++ > #67458 > unrolled thread
| Started by | peteolcott <Here@Home> |
|---|---|
| First post | 2019-08-08 12:15 -0500 |
| Last post | 2019-09-09 13:30 -0700 |
| Articles | 20 on this page of 100 — 16 participants |
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Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-08-08 12:15 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-08-08 21:28 +0100
Re: Provably unprovable eliminates incompleteness Dhu on Gate <campbell@neotext.ca> - 2019-09-08 06:06 +0000
Re: Provably unprovable eliminates incompleteness Stuart Redmann <DerTopper@web.de> - 2019-09-09 11:30 +0200
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 10:01 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibble@i42.removethisbit.co.uk> - 2019-09-09 21:38 +0100
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 18:05 -0500
Re: Provably unprovable eliminates incompleteness David Brown <david.brown@hesbynett.no> - 2019-09-10 09:01 +0200
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-10 10:38 -0500
Re: Provably unprovable eliminates incompleteness Reinhardt Behm <rbehm@hushmail.com> - 2019-09-11 15:31 +0800
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 12:04 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Reinhardt Behm <rbehm@hushmail.com> - 2019-09-12 10:20 +0800
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 23:51 -0500
[OT] Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-09-12 04:20 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Keith Thompson <kst-u@mib.org> - 2019-09-12 01:22 -0700
[OT] Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-09-11 19:52 -0700
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-12 22:07 +0000
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-12 18:53 -0500
Re: Provably unprovable eliminates incompleteness Keith Thompson <kst-u@mib.org> - 2019-09-12 17:47 -0700
[OT] Re: Provably unprovable eliminates incompleteness James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-09-12 19:00 -0700
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-13 08:14 +0000
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-13 09:35 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibble@i42.removethisbit.co.uk> - 2019-09-13 15:55 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 13:35 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-14 22:52 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 17:18 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-14 23:30 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 17:42 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Jeff Barnett <jbb@notatt.com> - 2019-09-14 18:12 -0600
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-15 08:09 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 09:50 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 17:13 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 11:24 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 17:30 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 12:08 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 18:15 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 13:35 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 20:02 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 14:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 22:26 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 18:11 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 18:12 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] guinness.tony@gmail.com - 2019-09-17 00:16 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-09-16 17:54 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-09-17 09:10 -0400
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-17 08:11 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 11:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-17 21:10 +0200
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 14:30 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-17 08:05 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 11:45 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-17 18:14 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 12:36 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 19:45 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-17 20:09 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 14:14 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 18:59 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Keith Thompson <kst-u@mib.org> - 2019-09-17 11:10 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 13:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Keith Thompson <kst-u@mib.org> - 2019-09-17 12:01 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-18 07:35 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Öö Tiib <ootiib@hot.ee> - 2019-09-18 04:22 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-18 15:41 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 10:02 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-18 22:25 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 16:41 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-18 22:56 +0100
[OT] Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-09-18 19:59 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-18 21:34 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 16:42 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-19 17:54 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 13:26 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:06 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:37 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 16:07 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:04 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 17:32 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:10 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:33 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 16:05 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:48 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 18:00 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-20 08:52 +0200
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-20 00:10 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-20 10:11 +0200
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:25 +0000
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:13 -0700
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:54 -0700
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-19 15:09 -0500
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:45 -0700
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:34 -0700
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] peteolcott <Here@Home> - 2019-09-19 14:58 -0500
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:57 -0700
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] peteolcott <Here@Home> - 2019-09-19 18:10 -0500
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-20 13:18 +0100
Re: Provably unprovable eliminates incompleteness Louis Valence <lvalence@example.com> - 2019-09-09 17:43 -0300
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:28 -0700
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-19 15:04 -0500
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 09:57 -0500
Re: Provably unprovable eliminates incompleteness Keith Thompson <kst-u@mib.org> - 2019-09-09 13:30 -0700
Page 4 of 5 — ← Prev page 1 2 3 [4] 5 Next page →
| From | Juha Nieminen <nospam@thanks.invalid> |
|---|---|
| Date | 2019-09-18 07:35 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qlsmo8$235h$1@adenine.netfront.net> |
| In reply to | #68473 |
In comp.lang.c++ peteolcott <Here@home> wrote: >> There is no "smallest real number larger than 0". Learn some number >> theory, will you? >> > > Keith Thompson proves that he fully understands the Infinitesimal > number system: Are you capable of understanding the "proof by contradiction" method in mathematics? Incidentally, the fact that there's no "smallest real number larger than 0" is one of the *classical* simple examples of applying proof by contradiction. "Infinitesimals", no matter how you define them, do not help here. You repeating your claims a million times does not change that fact.
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| From | Öö Tiib <ootiib@hot.ee> |
|---|---|
| Date | 2019-09-18 04:22 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <15ad8fb9-8ac7-45b8-8981-4bf2cc99fc47@googlegroups.com> |
| In reply to | #68488 |
On Wednesday, 18 September 2019 10:35:47 UTC+3, Juha Nieminen wrote: > In comp.lang.c++ peteolcott <Here@home> wrote: > >> There is no "smallest real number larger than 0". Learn some number > >> theory, will you? > >> > > > > Keith Thompson proves that he fully understands the Infinitesimal > > number system: > > Are you capable of understanding the "proof by contradiction" method in > mathematics? > > Incidentally, the fact that there's no "smallest real number larger than 0" > is one of the *classical* simple examples of applying proof by > contradiction. > > "Infinitesimals", no matter how you define them, do not help here. You > repeating your claims a million times does not change that fact. Replying to Peter Olcott seems not helping him to understand anything. BTW, is that about him?: https://www.youtube.com/watch?v=wfPPJBYc2B0
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| From | Mike Terry <news.dead.person.stones@darjeeling.plus.com> |
|---|---|
| Date | 2019-09-18 15:41 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <f6ydnVRewZK93x_AnZ2dnUU78YmdnZ2d@brightview.co.uk> |
| In reply to | #68494 |
On 18/09/2019 12:22, Öö Tiib wrote: > On Wednesday, 18 September 2019 10:35:47 UTC+3, Juha Nieminen wrote: >> In comp.lang.c++ peteolcott <Here@home> wrote: >>>> There is no "smallest real number larger than 0". Learn some number >>>> theory, will you? >>>> >>> >>> Keith Thompson proves that he fully understands the Infinitesimal >>> number system: >> >> Are you capable of understanding the "proof by contradiction" method in >> mathematics? >> >> Incidentally, the fact that there's no "smallest real number larger than 0" >> is one of the *classical* simple examples of applying proof by >> contradiction. >> >> "Infinitesimals", no matter how you define them, do not help here. You >> repeating your claims a million times does not change that fact. > > Replying to Peter Olcott seems not helping him to understand anything. > BTW, is that about him?: https://www.youtube.com/watch?v=wfPPJBYc2B0 > Yes.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-18 10:02 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <PYKdnZj3lqVg2x_AnZ2dnUU7-IWdnZ2d@giganews.com> |
| In reply to | #68488 |
On 9/18/2019 2:35 AM, Juha Nieminen wrote: > In comp.lang.c++ peteolcott <Here@home> wrote: >>> There is no "smallest real number larger than 0". Learn some number >>> theory, will you? >>> >> >> Keith Thompson proves that he fully understands the Infinitesimal >> number system: > > Are you capable of understanding the "proof by contradiction" method in > mathematics? > > Incidentally, the fact that there's no "smallest real number larger than 0" > is one of the *classical* simple examples of applying proof by > contradiction. > > "Infinitesimals", no matter how you define them, do not help here. You > repeating your claims a million times does not change that fact. > YES OF COURSE NOTHING HELPS WHEN YOU DON'T BOTHER TO READ WHAT IS SAID THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 On 9/16/2019 11:38 PM, Keith Thompson wrote: > we can define "iota" as an infinitesimal, something that is not a > real number but that has a location on the number line, directly > adjacent to the real number 0. It is greater than 0 and less than > any positive real number. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> |
|---|---|
| Date | 2019-09-18 22:25 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <FhxgF.182436$845.111634@fx19.fr7> |
| In reply to | #68499 |
On 18/09/2019 16:02, peteolcott wrote: > On 9/18/2019 2:35 AM, Juha Nieminen wrote: >> In comp.lang.c++ peteolcott <Here@home> wrote: >>>> There is no "smallest real number larger than 0". Learn some number >>>> theory, will you? >>>> >>> >>> Keith Thompson proves that he fully understands the Infinitesimal >>> number system: >> >> Are you capable of understanding the "proof by contradiction" method in >> mathematics? >> >> Incidentally, the fact that there's no "smallest real number larger than 0" >> is one of the *classical* simple examples of applying proof by >> contradiction. >> >> "Infinitesimals", no matter how you define them, do not help here. You >> repeating your claims a million times does not change that fact. >> > > YES OF COURSE NOTHING HELPS WHEN YOU DON'T BOTHER TO READ WHAT IS SAID > > THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 For the field of real numbers, no, there isn't. Take your meds. /Flibble -- "Snakes didn't evolve, instead talking snakes with legs changed into snakes." - Rick C. Hodgin “You won’t burn in hell. But be nice anyway.” – Ricky Gervais “I see Atheists are fighting and killing each other again, over who doesn’t believe in any God the most. Oh, no..wait.. that never happens.” – Ricky Gervais "Suppose it's all true, and you walk up to the pearly gates, and are confronted by God," Bryne asked on his show The Meaning of Life. "What will Stephen Fry say to him, her, or it?" "I'd say, bone cancer in children? What's that about?" Fry replied. "How dare you? How dare you create a world to which there is such misery that is not our fault. It's not right, it's utterly, utterly evil." "Why should I respect a capricious, mean-minded, stupid God who creates a world that is so full of injustice and pain. That's what I would say."
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-18 16:41 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <66CdnV-BbtTqOR_AnZ2dnUU7-IudnZ2d@giganews.com> |
| In reply to | #68514 |
On 9/18/2019 4:25 PM, Mr Flibble wrote: > On 18/09/2019 16:02, peteolcott wrote: >> On 9/18/2019 2:35 AM, Juha Nieminen wrote: >>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>> There is no "smallest real number larger than 0". Learn some number >>>>> theory, will you? >>>>> >>>> >>>> Keith Thompson proves that he fully understands the Infinitesimal >>>> number system: >>> >>> Are you capable of understanding the "proof by contradiction" method in >>> mathematics? >>> >>> Incidentally, the fact that there's no "smallest real number larger than 0" >>> is one of the *classical* simple examples of applying proof by >>> contradiction. >>> >>> "Infinitesimals", no matter how you define them, do not help here. You >>> repeating your claims a million times does not change that fact. >>> >> >> YES OF COURSE NOTHING HELPS WHEN YOU DON'T BOTHER TO READ WHAT IS SAID >> >> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 > > For the field of real numbers, no, there isn't. Take your meds. > > /Flibble > Did I say that it was a Real number? Quit being a jackass. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> |
|---|---|
| Date | 2019-09-18 22:56 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <fKxgF.60035$VR.34897@fx03.fr7> |
| In reply to | #68517 |
On 18/09/2019 22:41, peteolcott wrote: > On 9/18/2019 4:25 PM, Mr Flibble wrote: >> On 18/09/2019 16:02, peteolcott wrote: >>> On 9/18/2019 2:35 AM, Juha Nieminen wrote: >>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>>> There is no "smallest real number larger than 0". Learn some number >>>>>> theory, will you? >>>>>> >>>>> >>>>> Keith Thompson proves that he fully understands the Infinitesimal >>>>> number system: >>>> >>>> Are you capable of understanding the "proof by contradiction" method in >>>> mathematics? >>>> >>>> Incidentally, the fact that there's no "smallest real number larger >>>> than 0" >>>> is one of the *classical* simple examples of applying proof by >>>> contradiction. >>>> >>>> "Infinitesimals", no matter how you define them, do not help here. You >>>> repeating your claims a million times does not change that fact. >>>> >>> >>> YES OF COURSE NOTHING HELPS WHEN YOU DON'T BOTHER TO READ WHAT IS SAID >>> >>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >> >> For the field of real numbers, no, there isn't. Take your meds. >> >> /Flibble >> > > Did I say that it was a Real number? > Quit being a jackass. YOU CANNOT MIX NUMBERS FROM DIFFERENT FIELDS ON THE SAME NUMBER LINE YOU DEMENTED FUCKTARD. TAKE YOUR FUCKING MEDICATION. /Flibble -- "Snakes didn't evolve, instead talking snakes with legs changed into snakes." - Rick C. Hodgin “You won’t burn in hell. But be nice anyway.” – Ricky Gervais “I see Atheists are fighting and killing each other again, over who doesn’t believe in any God the most. Oh, no..wait.. that never happens.” – Ricky Gervais "Suppose it's all true, and you walk up to the pearly gates, and are confronted by God," Bryne asked on his show The Meaning of Life. "What will Stephen Fry say to him, her, or it?" "I'd say, bone cancer in children? What's that about?" Fry replied. "How dare you? How dare you create a world to which there is such misery that is not our fault. It's not right, it's utterly, utterly evil." "Why should I respect a capricious, mean-minded, stupid God who creates a world that is so full of injustice and pain. That's what I would say."
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| From | James Kuyper <jameskuyper@alumni.caltech.edu> |
|---|---|
| Date | 2019-09-18 19:59 -0700 |
| Subject | [OT] Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <a3e92b03-75af-4dbb-a343-01b38193eaf1@googlegroups.com> |
| In reply to | #68517 |
On Wednesday, September 18, 2019 at 5:41:28 PM UTC-4, peteolcott wrote: > On 9/18/2019 4:25 PM, Mr Flibble wrote: > > On 18/09/2019 16:02, peteolcott wrote: > >> On 9/18/2019 2:35 AM, Juha Nieminen wrote: > >>> In comp.lang.c++ peteolcott <Here@home> wrote: ... > >>>> Keith Thompson proves that he fully understands the Infinitesimal > >>>> number system: > >>> > >>> Are you capable of understanding the "proof by contradiction" method in > >>> mathematics? > >>> > >>> Incidentally, the fact that there's no "smallest real number larger than 0" > >>> is one of the *classical* simple examples of applying proof by > >>> contradiction. > >>> > >>> "Infinitesimals", no matter how you define them, do not help here. You > >>> repeating your claims a million times does not change that fact. > >>> > >> > >> YES OF COURSE NOTHING HELPS WHEN YOU DON'T BOTHER TO READ WHAT IS SAID > >> > >> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 > > > > For the field of real numbers, no, there isn't. Take your meds. > > > > /Flibble > > > > Did I say that it was a Real number? See <https://en.wikipedia.org/wiki/Number_line> "In basic mathematics, a number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by R. Every point of a number line is assumed to correspond to a real number, and every real number to a point." ... "In advanced mathematics, the expressions real number line, or real line are typically used to indicate the above-mentioned concept that every point on a straight line corresponds to a single real number, and vice versa." When you say that you're talking about the "number line", you're being, at best, confusing, and at worst, deliberately misleading, since if it contains things that aren't real numbers, then it isn't the "real number line" that most people think of when you say "number line". You should give your concept a special name to clearly distinguish it from the real number line. For the purposes of the following discussion, I'll call it the Olcott Number Line, ONL for short. Keith was not agreeing with you - he was pointing out an inherent limitation to your results due to the fact that you're talking about the ONL, rather than the conventional number line. You have not described your infinitesimals in any detail on this newsgroup, nor have you described how the ONL differs from the real number line. Your description of your a[i] notation doesn't make any sense when applied to the real number line, and what you haven't explained about the ONL means we can't be sure what it might mean when applied to the ONL. I don't have enough interest in your ideas to justify bothering to track down whether you've ever addressed those issues anywhere else. Depending upon those details that you haven't provided, it might be the case that you can prove that the ONL is countable. That in turn implies that the real numbers which are on the ONL are also countable; but that would not imply that the real numbers which aren't on the ONL are countable - that's the fundamental problem that you face. If the things you've said about the ONL are true (namely that 0.0[i] for i an integer from 1 to infinity generates every point on the ONL to the right of 0.0), then there must be real numbers which are not in the ONL - a lot of them - in fact, the infinitely overwhelming majority of real numbers cannot be on the ONL. Your description of your a[i] notation implies that that the real numbers in the ONL are ordered (I have no idea whether the infinitesimals are ordered, since you've provided no description of their properties). In other words, if a[i] and a[j] are both real, then a[i] < a[j] iff i < j. Is that true? If so, it's not only feasible, but trivial, to prove that most real numbers aren't on the ONL.
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| From | Juha Nieminen <nospam@thanks.invalid> |
|---|---|
| Date | 2019-09-18 21:34 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qlu7sk$11lg$1@adenine.netfront.net> |
| In reply to | #68499 |
In comp.lang.c++ peteolcott <Here@home> wrote: > THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 Ok, what is that number?
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-18 16:42 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <66CdnV6BbtQnOR_AnZ2dnUU7-IudnZ2d@giganews.com> |
| In reply to | #68516 |
On 9/18/2019 4:34 PM, Juha Nieminen wrote: > In comp.lang.c++ peteolcott <Here@home> wrote: >> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 > > Ok, what is that number? > It is the Infinitesimal Number 0.0[1] one point offset from 0.0. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Juha Nieminen <nospam@thanks.invalid> |
|---|---|
| Date | 2019-09-19 17:54 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qm0fd9$2f2u$1@adenine.netfront.net> |
| In reply to | #68518 |
In comp.lang.c++ peteolcott <Here@home> wrote: > On 9/18/2019 4:34 PM, Juha Nieminen wrote: >> In comp.lang.c++ peteolcott <Here@home> wrote: >>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >> >> Ok, what is that number? >> > > It is the Infinitesimal Number 0.0[1] one point offset from 0.0. What are the properties of that number that make it different from 0?
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 13:26 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <F_qdnSKXx8HMVR7AnZ2dnUU7-TfNnZ2d@giganews.com> |
| In reply to | #68526 |
On 9/19/2019 12:54 PM, Juha Nieminen wrote:
> In comp.lang.c++ peteolcott <Here@home> wrote:
>> On 9/18/2019 4:34 PM, Juha Nieminen wrote:
>>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0
>>>
>>> Ok, what is that number?
>>>
>>
>> It is the Infinitesimal Number 0.0[1] one point offset from 0.0.
>
> What are the properties of that number that make it different from 0?
>
[0, 1] - (0, 1] = {0} the first interval has exactly one point that the
second interval does not have, making the first interval Infinitesimally
longer than the second one.
The first interval begins at 0.0[0] and
The second interval begins at 0.0[1].
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | Juha Nieminen <nospam@thanks.invalid> |
|---|---|
| Date | 2019-09-20 08:06 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qm219l$1gk5$1@adenine.netfront.net> |
| In reply to | #68528 |
In comp.lang.c++ peteolcott <Here@home> wrote:
>> What are the properties of that number that make it different from 0?
>>
>
> [0, 1] - (0, 1] = {0} the first interval has exactly one point that the
> second interval does not have, making the first interval Infinitesimally
> longer than the second one.
>
> The first interval begins at 0.0[0] and
> The second interval begins at 0.0[1].
You didn't give a single property of that number. You only made claims
about an interval.
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 13:37 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <chine.bleu-D7B704.13370419092019@reader.eternal-september.org> |
| In reply to | #68499 |
In article <PYKdnZj3lqVg2x_AnZ2dnUU7-IWdnZ2d@giganews.com>, peteolcott <Here@Home> wrote: > On 9/18/2019 2:35 AM, Juha Nieminen wrote: > > In comp.lang.c++ peteolcott <Here@home> wrote: > >>> There is no "smallest real number larger than 0". Learn some number > >>> theory, will you? > >>> > >> > >> Keith Thompson proves that he fully understands the Infinitesimal > >> number system: > > > > Are you capable of understanding the "proof by contradiction" method in > > mathematics? > > > > Incidentally, the fact that there's no "smallest real number larger than 0" > > is one of the *classical* simple examples of applying proof by > > contradiction. > > > > "Infinitesimals", no matter how you define them, do not help here. You > > repeating your claims a million times does not change that fact. > > > > YES OF COURSE NOTHING HELPS WHEN YOU DON'T BOTHER TO READ WHAT IS SAID > > THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 > On 9/16/2019 11:38 PM, Keith Thompson wrote: > > we can define "iota" as an infinitesimal, something that is not a > > real number but that has a location on the number line, directly > > adjacent to the real number 0. It is greater than 0 and less than > > any positive real number. Unless you can prove the set of numbers satisfying this definition is finite, all you're doing is adding another infinite set to the issue. Hint: it's an infinite set. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 16:07 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <m6ydnRGwy51ucB7AnZ2dnUU7-KudnZ2d@giganews.com> |
| In reply to | #68539 |
On 9/19/2019 3:37 PM, Siri Cruise wrote: > In article <PYKdnZj3lqVg2x_AnZ2dnUU7-IWdnZ2d@giganews.com>, > peteolcott <Here@Home> wrote: > >> On 9/18/2019 2:35 AM, Juha Nieminen wrote: >>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>> There is no "smallest real number larger than 0". Learn some number >>>>> theory, will you? >>>>> >>>> >>>> Keith Thompson proves that he fully understands the Infinitesimal >>>> number system: >>> >>> Are you capable of understanding the "proof by contradiction" method in >>> mathematics? >>> >>> Incidentally, the fact that there's no "smallest real number larger than 0" >>> is one of the *classical* simple examples of applying proof by >>> contradiction. >>> >>> "Infinitesimals", no matter how you define them, do not help here. You >>> repeating your claims a million times does not change that fact. >>> >> >> YES OF COURSE NOTHING HELPS WHEN YOU DON'T BOTHER TO READ WHAT IS SAID >> >> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >> On 9/16/2019 11:38 PM, Keith Thompson wrote: >> > we can define "iota" as an infinitesimal, something that is not a >> > real number but that has a location on the number line, directly >> > adjacent to the real number 0. It is greater than 0 and less than >> > any positive real number. > > Unless you can prove the set of numbers satisfying this definition is finite, > all you're doing is adding another infinite set to the issue. > > Hint: it's an infinite set. > If all of the points on the number line can be counted using integers then all infinite sets have the same cardinality. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 15:04 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <chine.bleu-22793B.15040719092019@reader.eternal-september.org> |
| In reply to | #68541 |
In article <m6ydnRGwy51ucB7AnZ2dnUU7-KudnZ2d@giganews.com>, peteolcott <Here@Home> wrote: > If all of the points on the number line can be counted using integers > then all infinite sets have the same cardinality. They can't be. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 17:32 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <d6udncquBISMnxnAnZ2dnUU7-a2dnZ2d@giganews.com> |
| In reply to | #68542 |
On 9/19/2019 5:04 PM, Siri Cruise wrote: > In article <m6ydnRGwy51ucB7AnZ2dnUU7-KudnZ2d@giganews.com>, > peteolcott <Here@Home> wrote: > >> If all of the points on the number line can be counted using integers >> then all infinite sets have the same cardinality. > > They can't be. > I already proved this in other replies to you. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Juha Nieminen <nospam@thanks.invalid> |
|---|---|
| Date | 2019-09-20 08:10 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qm21he$1gk5$2@adenine.netfront.net> |
| In reply to | #68544 |
In comp.lang.c++ peteolcott <Here@home> wrote: > On 9/19/2019 5:04 PM, Siri Cruise wrote: >> In article <m6ydnRGwy51ucB7AnZ2dnUU7-KudnZ2d@giganews.com>, >> peteolcott <Here@Home> wrote: >> >>> If all of the points on the number line can be counted using integers >>> then all infinite sets have the same cardinality. >> >> They can't be. >> > > I already proved this in other replies to you. No, you didn't. Making a claim is not a mathematical proof.
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 13:33 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <chine.bleu-228BC9.13325719092019@reader.eternal-september.org> |
| In reply to | #68473 |
In article <O9udnZdFPogAkBzAnZ2dnUU7-c3NnZ2d@giganews.com>, peteolcott <Here@Home> wrote: > Keith Thompson proves that he fully understands the Infinitesimal > number system: > > On 9/16/2019 11:38 PM, Keith Thompson wrote: > > I can imagine that *this* set has a least element. For example > > we can define "iota" as an infinitesimal, something that is not a > > real number but that has a location on the number line, directly > > adjacent to the real number 0. It is greater than 0 and less than > > any positive real number. iota > iota^2 > iota^3 > ... > He elaborates this understanding much more completely in his > 9/16/2019 11:38 PM, reply. Infinitesimals cannot be reals. A couple of centuries ago it was shown this leads to inconsistency. Recently nonstandard analysis has reintroduced infinitesimals and their reciprocals. Positive infinitesimals are an infinite set each greater than zero and less than any positive real. Their reciprocals are greater than any real number and defined since infinitesimals are nonzero. Note that for an infinitesimal dx, dx > dx^2 > dx^3 > ... . So with the usual < infinitesimals also lack a minimum element. Choice assumes an order exists, but we haven't found it. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 16:05 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <m6ydnRawy53gcB7AnZ2dnUU7-KvNnZ2d@giganews.com> |
| In reply to | #68538 |
On 9/19/2019 3:33 PM, Siri Cruise wrote: > In article <O9udnZdFPogAkBzAnZ2dnUU7-c3NnZ2d@giganews.com>, > peteolcott <Here@Home> wrote: > >> Keith Thompson proves that he fully understands the Infinitesimal >> number system: >> >> On 9/16/2019 11:38 PM, Keith Thompson wrote: >> > I can imagine that *this* set has a least element. For example >> > we can define "iota" as an infinitesimal, something that is not a >> > real number but that has a location on the number line, directly >> > adjacent to the real number 0. It is greater than 0 and less than >> > any positive real number. > > iota > iota^2 > iota^3 > ... > >> He elaborates this understanding much more completely in his >> 9/16/2019 11:38 PM, reply. > > Infinitesimals cannot be reals. A couple of centuries ago it was shown this > leads to inconsistency. Recently nonstandard analysis has reintroduced > infinitesimals and their reciprocals. Positive infinitesimals are an infinite > set each greater than zero and less than any positive real. Their reciprocals > are greater than any real number and defined since infinitesimals are nonzero. > > Note that for an infinitesimal dx, dx > dx^2 > dx^3 > ... . So with the usual < > infinitesimals also lack a minimum element. Choice assumes an order exists, but > we haven't found it. > This is the Pete Olcott copyright 2018, 2019 notion of infinitesimals that have a bijection to every point on the number line indexed by integers. Reals have no point immediately adjacent to 0.0, infinitesimals name this point 0.0[1]. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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