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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
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 18:11 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <y-GdnUeSA6QOix3AnZ2dnUU7-VfNnZ2d@giganews.com> |
| In reply to | #68459 |
On 9/16/2019 4:26 PM, Mr Flibble wrote: > On 16/09/2019 20:48, peteolcott wrote: >> On 9/16/2019 2:02 PM, Mr Flibble wrote: >>> On 16/09/2019 19:35, peteolcott wrote: >>>> On 9/16/2019 12:15 PM, Mr Flibble wrote: >>>>> On 16/09/2019 18:08, peteolcott wrote: >>>>>> On 9/16/2019 11:30 AM, Mr Flibble wrote: >>>>>>> On 16/09/2019 17:24, peteolcott wrote: >>>>>>>> On 9/16/2019 11:13 AM, Mr Flibble wrote: >>>>>>>>> On 16/09/2019 15:50, peteolcott wrote: >>>>>>>>>> On 9/15/2019 3:09 AM, Juha Nieminen wrote: >>>>>>>>>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>>>>>>>>> On 9/13/2019 3:14 AM, Juha Nieminen wrote: >>>>>>>>>>>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>>>>>>>>>>> There is a contiguous set of points between (3.0, 4.0]. >>>>>>>>>>>>>> There is a first point in that interval, let's call it X. >>>>>>>>>>>>> >>>>>>>>>>>>> No, there isn't. Such a point doesn't exist. >>>>>>>>>>>>> >>>>>>>>>>>>> Learn some number theory, will you? >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> APPARENTLY I AM RIGHT AND YOU ARE WRONG!!! >>>>>>>>>>>> >>>>>>>>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>>>>>>>> >>>>>>>>>>> You are right and I'm wrong, even though that website does not >>>>>>>>>>> say what you are saying? >>>>>>>>>>> >>>>>>>>>>> It doesn't matter how many arguments you present or how much you >>>>>>>>>>> shout, it will not make "the smallest real number larger than 3" >>>>>>>>>>> to start to exist. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> The length of this interval is exactly 3.0 >>>>>>>>>> (0.0, 3.0] >>>>>>>>>> The smallest real number larger than 0.0 is its first point. >>>>>>>>> >>>>>>>>> There isn't a smallest real number larger than 0.0; it is impossible for such a number to exist. >>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>>>>> An interval (open interval) is a set of points on a line lying between two fixed >>>>>>>> points A and B, where A and B themselves are considered not to belong to the interval. >>>>>>>> >>>>>>>> Since [0, 100) clearly specifies every point on the number line between >>>>>>>> 0 and 100 except 100 it is specifying the point immediately before 100 >>>>>>>> as the last point of this interval with no points in-between this point >>>>>>>> and 100. THAT IS WHAT IT SAYS. >>>>>>>> >>>>>>>> This contradicts the definition of real numbers that specifies there >>>>>>>> is always a real number between every pair of real numbers. >>>>>>> >>>>>>> Points have a "width" of zero, dear. Please take your meds. >>>>>>> >>>>>>> /Flibble >>>>>>> >>>>>> >>>>>> The relation between real numbers and points on a number line is defined inconsistently. >>>>>> >>>>>> >> An interval (open interval) is a set of points on a line lying between two fixed >>>>>> >> points A and B, where A and B themselves are considered not to belong to the interval. >>>>>> >>>>>> The above stipulates all of the points between A and B besides A and B thus >>>>>> the first point AFTER A (with no points in-between) and the first point >>>>>> BEFORE B (with no points in-between) ARE SPECIFIED in this interval. >>>>> >>>>> That definition is entirely consistent with points having a "width" of zero, dear. Please take your meds so you can spare us any more demented posts. >>>>> >>>>> /Flibble >>>>> >>>> >>>> (A) An open interval specifies its first point as immediately after a >>>> specified point with no points in-between. >>>> >>>> (B) The definition of real numbers says there are always points in-between. >>>> >>>> (A) contradicts (B). >>> >>> (A) is erroneous, you made "immediately after" and "no points in-between" up based on nothing but your demented thoughts and reasoning. Take your meds. >>> >>> /Flibble >>> >> >> You aren't bright enough to actually follow the reasoning. >> You can only spout off what you learned by rote. >> >> A number line has an infinite set of contiguous ascending points. >> When you remove the very first point of an interval [0, 1] you are >> left with an interval beginning with the very next point (0, 1]. >> >> Even if every other aspect of mathematics disagrees, none-the-less the >> beginning of this interval: (0, 1] stipulates the point immediately after 0. >> If every other aspect of mathematics says no such point exists, >> none-the-less it is defined to exist by the definition of open interval. >> >> Learned-by-rote people are not bright enough to discern new innovations. >> To them any new idea is always incorrect because it is unconventional. >> They simply are not bright enough to process reasoning instead they >> merely look up the "facts" of conventional wisdom. > > This is the most perfect example of projection that I have ever seen. > > /Flibble > My position is diametrically opposed to the learned-by-rote position thus proving that I did not learn it by rote. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 18:12 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <y-GdnUaSA6RPix3AnZ2dnUU7-VednZ2d@giganews.com> |
| In reply to | #68460 |
On 9/16/2019 6:11 PM, peteolcott wrote: > On 9/16/2019 4:26 PM, Mr Flibble wrote: >> On 16/09/2019 20:48, peteolcott wrote: >>> On 9/16/2019 2:02 PM, Mr Flibble wrote: >>>> On 16/09/2019 19:35, peteolcott wrote: >>>>> On 9/16/2019 12:15 PM, Mr Flibble wrote: >>>>>> On 16/09/2019 18:08, peteolcott wrote: >>>>>>> On 9/16/2019 11:30 AM, Mr Flibble wrote: >>>>>>>> On 16/09/2019 17:24, peteolcott wrote: >>>>>>>>> On 9/16/2019 11:13 AM, Mr Flibble wrote: >>>>>>>>>> On 16/09/2019 15:50, peteolcott wrote: >>>>>>>>>>> On 9/15/2019 3:09 AM, Juha Nieminen wrote: >>>>>>>>>>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>>>>>>>>>> On 9/13/2019 3:14 AM, Juha Nieminen wrote: >>>>>>>>>>>>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>>>>>>>>>>>> There is a contiguous set of points between (3.0, 4.0]. >>>>>>>>>>>>>>> There is a first point in that interval, let's call it X. >>>>>>>>>>>>>> >>>>>>>>>>>>>> No, there isn't. Such a point doesn't exist. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Learn some number theory, will you? >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> APPARENTLY I AM RIGHT AND YOU ARE WRONG!!! >>>>>>>>>>>>> >>>>>>>>>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>>>>>>>>> >>>>>>>>>>>> You are right and I'm wrong, even though that website does not >>>>>>>>>>>> say what you are saying? >>>>>>>>>>>> >>>>>>>>>>>> It doesn't matter how many arguments you present or how much you >>>>>>>>>>>> shout, it will not make "the smallest real number larger than 3" >>>>>>>>>>>> to start to exist. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> The length of this interval is exactly 3.0 >>>>>>>>>>> (0.0, 3.0] >>>>>>>>>>> The smallest real number larger than 0.0 is its first point. >>>>>>>>>> >>>>>>>>>> There isn't a smallest real number larger than 0.0; it is impossible for such a number to exist. >>>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>>>>>> An interval (open interval) is a set of points on a line lying between two fixed >>>>>>>>> points A and B, where A and B themselves are considered not to belong to the interval. >>>>>>>>> >>>>>>>>> Since [0, 100) clearly specifies every point on the number line between >>>>>>>>> 0 and 100 except 100 it is specifying the point immediately before 100 >>>>>>>>> as the last point of this interval with no points in-between this point >>>>>>>>> and 100. THAT IS WHAT IT SAYS. >>>>>>>>> >>>>>>>>> This contradicts the definition of real numbers that specifies there >>>>>>>>> is always a real number between every pair of real numbers. >>>>>>>> >>>>>>>> Points have a "width" of zero, dear. Please take your meds. >>>>>>>> >>>>>>>> /Flibble >>>>>>>> >>>>>>> >>>>>>> The relation between real numbers and points on a number line is defined inconsistently. >>>>>>> >>>>>>> >> An interval (open interval) is a set of points on a line lying between two fixed >>>>>>> >> points A and B, where A and B themselves are considered not to belong to the interval. >>>>>>> >>>>>>> The above stipulates all of the points between A and B besides A and B thus >>>>>>> the first point AFTER A (with no points in-between) and the first point >>>>>>> BEFORE B (with no points in-between) ARE SPECIFIED in this interval. >>>>>> >>>>>> That definition is entirely consistent with points having a "width" of zero, dear. Please take your meds so you can spare us any more demented posts. >>>>>> >>>>>> /Flibble >>>>>> >>>>> >>>>> (A) An open interval specifies its first point as immediately after a >>>>> specified point with no points in-between. >>>>> >>>>> (B) The definition of real numbers says there are always points in-between. >>>>> >>>>> (A) contradicts (B). >>>> >>>> (A) is erroneous, you made "immediately after" and "no points in-between" up based on nothing but your demented thoughts and reasoning. Take your meds. >>>> >>>> /Flibble >>>> >>> >>> You aren't bright enough to actually follow the reasoning. >>> You can only spout off what you learned by rote. >>> >>> A number line has an infinite set of contiguous ascending points. >>> When you remove the very first point of an interval [0, 1] you are >>> left with an interval beginning with the very next point (0, 1]. >>> >>> Even if every other aspect of mathematics disagrees, none-the-less the >>> beginning of this interval: (0, 1] stipulates the point immediately after 0. >>> If every other aspect of mathematics says no such point exists, >>> none-the-less it is defined to exist by the definition of open interval. >>> >>> Learned-by-rote people are not bright enough to discern new innovations. >>> To them any new idea is always incorrect because it is unconventional. >>> They simply are not bright enough to process reasoning instead they >>> merely look up the "facts" of conventional wisdom. >> >> This is the most perfect example of projection that I have ever seen. >> >> /Flibble >> > > My position is diametrically opposed to the learned-by-rote position > thus proving that I did not learn it by rote. > You would have to double your wits to become a halfwit. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | guinness.tony@gmail.com |
|---|---|
| Date | 2019-09-17 00:16 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <7b369cb9-37e6-4b50-bfd4-56d1463b4eed@googlegroups.com> |
| In reply to | #68460 |
On Tuesday, 17 September 2019 00:11:29 UTC+1, peteolcott wrote: > On 9/16/2019 4:26 PM, Mr Flibble wrote: > > On 16/09/2019 20:48, peteolcott wrote: > >> On 9/16/2019 2:02 PM, Mr Flibble wrote: > >>> On 16/09/2019 19:35, peteolcott wrote: > >>>> On 9/16/2019 12:15 PM, Mr Flibble wrote: > >>>>> On 16/09/2019 18:08, peteolcott wrote: > >>>>>> On 9/16/2019 11:30 AM, Mr Flibble wrote: > >>>>>>> On 16/09/2019 17:24, peteolcott wrote: > >>>>>>>> On 9/16/2019 11:13 AM, Mr Flibble wrote: > >>>>>>>>> On 16/09/2019 15:50, peteolcott wrote: > >>>>>>>>>> On 9/15/2019 3:09 AM, Juha Nieminen wrote: > >>>>>>>>>>> In comp.lang.c++ peteolcott <Here@home> wrote: > >>>>>>>>>>>> On 9/13/2019 3:14 AM, Juha Nieminen wrote: > >>>>>>>>>>>>> In comp.lang.c++ peteolcott <Here@home> wrote: > >>>>>>>>>>>>>> There is a contiguous set of points between (3.0, 4.0]. > >>>>>>>>>>>>>> There is a first point in that interval, let's call it X. > >>>>>>>>>>>>> > >>>>>>>>>>>>> No, there isn't. Such a point doesn't exist. > >>>>>>>>>>>>> > >>>>>>>>>>>>> Learn some number theory, will you? > >>>>>>>>>>>>> > >>>>>>>>>>>> > >>>>>>>>>>>> APPARENTLY I AM RIGHT AND YOU ARE WRONG!!! > >>>>>>>>>>>> > >>>>>>>>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment > >>>>>>>>>>> > >>>>>>>>>>> You are right and I'm wrong, even though that website does not > >>>>>>>>>>> say what you are saying? > >>>>>>>>>>> > >>>>>>>>>>> It doesn't matter how many arguments you present or how much you > >>>>>>>>>>> shout, it will not make "the smallest real number larger than 3" > >>>>>>>>>>> to start to exist. > >>>>>>>>>>> > >>>>>>>>>> > >>>>>>>>>> The length of this interval is exactly 3.0 > >>>>>>>>>> (0.0, 3.0] > >>>>>>>>>> The smallest real number larger than 0.0 is its first point. > >>>>>>>>> > >>>>>>>>> There isn't a smallest real number larger than 0.0; it is impossible for such a number to exist. > >>>>>>>>> > >>>>>>>> > >>>>>>>> > >>>>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment > >>>>>>>> An interval (open interval) is a set of points on a line lying between two fixed > >>>>>>>> points A and B, where A and B themselves are considered not to belong to the interval. > >>>>>>>> > >>>>>>>> Since [0, 100) clearly specifies every point on the number line between > >>>>>>>> 0 and 100 except 100 it is specifying the point immediately before 100 > >>>>>>>> as the last point of this interval with no points in-between this point > >>>>>>>> and 100. THAT IS WHAT IT SAYS. > >>>>>>>> > >>>>>>>> This contradicts the definition of real numbers that specifies there > >>>>>>>> is always a real number between every pair of real numbers. > >>>>>>> > >>>>>>> Points have a "width" of zero, dear. Please take your meds. > >>>>>>> > >>>>>>> /Flibble > >>>>>>> > >>>>>> > >>>>>> The relation between real numbers and points on a number line is defined inconsistently. > >>>>>> > >>>>>> >> An interval (open interval) is a set of points on a line lying between two fixed > >>>>>> >> points A and B, where A and B themselves are considered not to belong to the interval. > >>>>>> > >>>>>> The above stipulates all of the points between A and B besides A and B thus > >>>>>> the first point AFTER A (with no points in-between) and the first point > >>>>>> BEFORE B (with no points in-between) ARE SPECIFIED in this interval. > >>>>> > >>>>> That definition is entirely consistent with points having a "width" of zero, dear. Please take your meds so you can spare us any more demented posts. > >>>>> > >>>>> /Flibble > >>>>> > >>>> > >>>> (A) An open interval specifies its first point as immediately after a > >>>> specified point with no points in-between. > >>>> > >>>> (B) The definition of real numbers says there are always points in-between. > >>>> > >>>> (A) contradicts (B). > >>> > >>> (A) is erroneous, you made "immediately after" and "no points in-between" up based on nothing but your demented thoughts and reasoning. Take your meds. > >>> > >>> /Flibble > >>> > >> > >> You aren't bright enough to actually follow the reasoning. > >> You can only spout off what you learned by rote. > >> > >> A number line has an infinite set of contiguous ascending points. > >> When you remove the very first point of an interval [0, 1] you are > >> left with an interval beginning with the very next point (0, 1]. > >> > >> Even if every other aspect of mathematics disagrees, none-the-less the > >> beginning of this interval: (0, 1] stipulates the point immediately after 0. > >> If every other aspect of mathematics says no such point exists, > >> none-the-less it is defined to exist by the definition of open interval. > >> > >> Learned-by-rote people are not bright enough to discern new innovations. > >> To them any new idea is always incorrect because it is unconventional. > >> They simply are not bright enough to process reasoning instead they > >> merely look up the "facts" of conventional wisdom. > > > > This is the most perfect example of projection that I have ever seen. > > > > /Flibble > > > > My position is diametrically opposed to the learned-by-rote position > thus proving that I did not learn it by rote. If you omitted those last three words you would be correct.
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| From | James Kuyper <jameskuyper@alumni.caltech.edu> |
|---|---|
| Date | 2019-09-16 17:54 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <4745e650-3e4c-403d-8602-b4bf449982a4@googlegroups.com> |
| In reply to | #68458 |
On Monday, September 16, 2019 at 3:48:38 PM UTC-4, peteolcott wrote:
...
> Even if every other aspect of mathematics disagrees, none-the-less the
> beginning of this interval: (0, 1] stipulates the point immediately after 0.
> If every other aspect of mathematics says no such point exists,
> none-the-less it is defined to exist by the definition of open interval.
No, the definition of an open interval is explicitly based upon the
absence of such a point. See
<https://en.wikipedia.org/wiki/Interval_(mathematics)#Terminology>:
123456789012345678901234567890123456789012345678901234567890123456789012
"An interval is said to be left-open if and only if it contains no
minimum (an element that is smaller than all other elements); right-open
if it contains no maximum; and open if it has both properties. The
interval [0,1) = {x | 0 ≤ x < 1}, for example, is left-closed and right-
open. The empty set and the set of all reals are open intervals, while
the set of non-negative reals, for example, is a right-open but not
left-open interval."
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| From | James Kuyper <jameskuyper@alumni.caltech.edu> |
|---|---|
| Date | 2019-09-17 09:10 -0400 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qlqm0l$h32$1@dont-email.me> |
| In reply to | #68463 |
On 9/16/19 8:54 PM, James Kuyper wrote: > On Monday, September 16, 2019 at 3:48:38 PM UTC-4, peteolcott wrote: > ... >> Even if every other aspect of mathematics disagrees, none-the-less the >> beginning of this interval: (0, 1] stipulates the point immediately after 0. >> If every other aspect of mathematics says no such point exists, >> none-the-less it is defined to exist by the definition of open interval. > > No, the definition of an open interval is explicitly based upon the > absence of such a point. See > <https://en.wikipedia.org/wiki/Interval_(mathematics)#Terminology>: > > "An interval is said to be left-open if and only if it contains no > minimum (an element that is smaller than all other elements); right-open > if it contains no maximum; and open if it has both properties. ... I realized a few additional points after posting that message. If, as you claim, the interval (0, 1] contains a minimum value (let's call it iota, for convenience), then it is, by definition (see above) left-closed, not left-open. Therefore, that interval can be written as [iota, 1]. Now, since 0 < iota and iota < 1, (0, 1] is the union of (0, iota) and [iota, 1]. Your claim is equivalent, therefore, to the claim that (0, iota) is the empty set. But the Lesbesgue measure of (0, iota) is iota - 0, or simply iota. Since iota > 0, the interval (0, iota) can't empty. Furthermore, the Lesbesgue measure of (0, 1] is 1 - 0 = 1, whereas the Lesbesgue measure of [iota, 1] is 1 - iota. Since 0 < iota, 1 - iota < 1. Since (0, 1] and [iota, 1] have different measures, they can't be the same set. For any point x in (iota, 1), since 0 < iota < x < 1, the value y = iota*(x - iota)/(1 - iota) is real, greater than 0, and less than iota. In other words, it is an element of (0, iota). Therefore, the claim that (0, 1] contains a minimum value leads to a contradiction, because every value of y is in the interval (0, 1], and is less than iota. Note that in the above paragraph I was referring to the open interval (iota, 1), not the closed interval [iota,1] - don't get confused about the difference between the two intervals. I specified that open interval because the claims I made about y would not be true for x=iota or x=1.
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| From | Juha Nieminen <nospam@thanks.invalid> |
|---|---|
| Date | 2019-09-17 08:11 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qlq4f5$55s$1@adenine.netfront.net> |
| In reply to | #68458 |
In comp.lang.c++ peteolcott <Here@home> wrote: > Even if every other aspect of mathematics disagrees, none-the-less the > beginning of this interval: (0, 1] stipulates the point immediately after 0. There is no point immediately after 0. You might be incapable of comprehending such a fact of mathematics, but that doesn't mean it's incorrect. An open interval does not mean that there must exist a particular number at the end of that interval. There is no such number. You cannot give its value as it's conceptually and mathematically non-existent. It doesn't exist even in some kind of abstract meta-sense. It doesn't exist even if you introduce the concept of "infinitesimal" into your number system (no matter how you define "infinitesimal"). Positing that there exists such a number leads immediately to a contradiction, and it's extraordinarily simple to prove that. Since the assumption was that the number exists, but that assumption leads to a contradiction, that means that the assumption was incorrect. "Proof by contradiction" is not just some wishy-washy nebulous term.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 11:48 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <O9udnZZFPoiikxzAnZ2dnUU7-c1QAAAA@giganews.com> |
| In reply to | #68470 |
On 9/17/2019 3:11 AM, Juha Nieminen wrote: > In comp.lang.c++ peteolcott <Here@home> wrote: >> Even if every other aspect of mathematics disagrees, none-the-less the >> beginning of this interval: (0, 1] stipulates the point immediately after 0. > > There is no point immediately after 0. You might be incapable of > comprehending such a fact of mathematics, but that doesn't mean > it's incorrect. > > An open interval does not mean that there must exist a particular > number at the end of that interval. There is no such number. You cannot > give its value as it's conceptually and mathematically non-existent. > It doesn't exist even in some kind of abstract meta-sense. It doesn't > exist even if you introduce the concept of "infinitesimal" into your > number system (no matter how you define "infinitesimal"). > > Positing that there exists such a number leads immediately to a > contradiction, and it's extraordinarily simple to prove that. > Since the assumption was that the number exists, but that assumption > leads to a contradiction, that means that the assumption was incorrect. > "Proof by contradiction" is not just some wishy-washy nebulous term. > On 9/16/2019 11:38 PM, Keith Thompson wrote: > Arbitrarily inventing a new notation, let _(0,1]_ be a set of, um, > something or other. It includes all the real numbers in (0,1], > and it may also include some other things, each of which is greater > than 0, less than or equal to 1, and somewhere on the "number line" > between 0 and 1. Some of the non-real elements might be points, > or infinitesimals. I'll assert that for any two members of *this* > set, exactly one of a<b, a=b, a>b is true. > > 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. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2019-09-17 21:10 +0200 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qlrb3p$ipv$1@dont-email.me> |
| In reply to | #68474 |
On 17/09/2019 18:48, peteolcott wrote: > On 9/17/2019 3:11 AM, Juha Nieminen wrote: >> In comp.lang.c++ peteolcott <Here@home> wrote: >>> Even if every other aspect of mathematics disagrees, none-the-less the >>> beginning of this interval: (0, 1] stipulates the point immediately >>> after 0. >> >> There is no point immediately after 0. You might be incapable of >> comprehending such a fact of mathematics, but that doesn't mean >> it's incorrect. >> >> An open interval does not mean that there must exist a particular >> number at the end of that interval. There is no such number. You cannot >> give its value as it's conceptually and mathematically non-existent. >> It doesn't exist even in some kind of abstract meta-sense. It doesn't >> exist even if you introduce the concept of "infinitesimal" into your >> number system (no matter how you define "infinitesimal"). >> >> Positing that there exists such a number leads immediately to a >> contradiction, and it's extraordinarily simple to prove that. >> Since the assumption was that the number exists, but that assumption >> leads to a contradiction, that means that the assumption was incorrect. >> "Proof by contradiction" is not just some wishy-washy nebulous term. >> > > > On 9/16/2019 11:38 PM, Keith Thompson wrote: > > Arbitrarily inventing a new notation, let _(0,1]_ be a set of, um, > > something or other. It includes all the real numbers in (0,1], > > and it may also include some other things, each of which is greater > > than 0, less than or equal to 1, and somewhere on the "number line" > > between 0 and 1. Some of the non-real elements might be points, > > or infinitesimals. I'll assert that for any two members of *this* > > set, exactly one of a<b, a=b, a>b is true. > > > > 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. > You can always define extra elements and add them to sets like this. But you can't do so in a way that is consistent in other ways. So you can make the ordered set of "real in (0, 1] plus iota", but you lose other properties of the reals. "reals plus iota" is not a field, nor is it complete. And it does not make sense to talk about "having a location on the number line" without defining "the number line" - normally that term is used precisely to mean the real numbers.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 14:30 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] |
| Message-ID | <FZ6dnWxKU5GkqRzAnZ2dnUU7-bvNnZ2d@giganews.com> |
| In reply to | #68483 |
On 9/17/2019 2:10 PM, David Brown wrote:
> On 17/09/2019 18:48, peteolcott wrote:
>> On 9/17/2019 3:11 AM, Juha Nieminen wrote:
>>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>>> Even if every other aspect of mathematics disagrees, none-the-less the
>>>> beginning of this interval: (0, 1] stipulates the point immediately after 0.
>>>
>>> There is no point immediately after 0. You might be incapable of
>>> comprehending such a fact of mathematics, but that doesn't mean
>>> it's incorrect.
>>>
>>> An open interval does not mean that there must exist a particular
>>> number at the end of that interval. There is no such number. You cannot
>>> give its value as it's conceptually and mathematically non-existent.
>>> It doesn't exist even in some kind of abstract meta-sense. It doesn't
>>> exist even if you introduce the concept of "infinitesimal" into your
>>> number system (no matter how you define "infinitesimal").
>>>
>>> Positing that there exists such a number leads immediately to a
>>> contradiction, and it's extraordinarily simple to prove that.
>>> Since the assumption was that the number exists, but that assumption
>>> leads to a contradiction, that means that the assumption was incorrect.
>>> "Proof by contradiction" is not just some wishy-washy nebulous term.
>>>
>>
>>
>> On 9/16/2019 11:38 PM, Keith Thompson wrote:
>> > Arbitrarily inventing a new notation, let _(0,1]_ be a set of, um,
>> > something or other. It includes all the real numbers in (0,1],
>> > and it may also include some other things, each of which is greater
>> > than 0, less than or equal to 1, and somewhere on the "number line"
>> > between 0 and 1. Some of the non-real elements might be points,
>> > or infinitesimals. I'll assert that for any two members of *this*
>> > set, exactly one of a<b, a=b, a>b is true.
>> >
>> > 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.
>>
>
> You can always define extra elements and add them to sets like this. But you can't do so in a way that is consistent in other ways. So you can make the ordered set of "real in (0, 1] plus iota", but you lose other properties of the reals. "reals plus
> iota" is not a field, nor is it complete.
>
> And it does not make sense to talk about "having a location on the number line" without defining "the number line" - normally that term is used precisely to mean the real numbers.
>
This is not Keith and Mike's ideas it is their agreement with my ideas:
These are the two key essences of agreement with Infinitesimal Numbers:
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.
On 9/16/2019 8:33 PM, Mike Terry wrote:
> OK, so (A,B] = [A,B] - {A}, and that can be counted as an "operation
in which we get (A,B] from [A,B].
Here are some examples of the next level of elaboration based on the
above two key essences of agreement:
Mike Terry agreed with this verbatim: [A, B] - {A} = (A, B]
Infinitesimal Numbers would encode (A, B] as [A[1], B]
We merely extrapolate the very next elaboration
[A[1], B] - {A[1]} = (A[1], B] encoded as [A[2], B]
--
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 | 2019-09-17 08:05 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qlq440$3ar$1@adenine.netfront.net> |
| In reply to | #68447 |
In comp.lang.c++ peteolcott <Here@home> wrote: > The length of this interval is exactly 3.0 > (0.0, 3.0] > The smallest real number larger than 0.0 is its first point. You can repeat that as many times as you want, but that will not make such a number to exist. There is no "smallest real number larger than 0". Learn some number theory, will you?
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 11:45 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <O9udnZdFPogAkBzAnZ2dnUU7-c3NnZ2d@giganews.com> |
| In reply to | #68469 |
On 9/17/2019 3:05 AM, Juha Nieminen wrote: > In comp.lang.c++ peteolcott <Here@home> wrote: >> The length of this interval is exactly 3.0 >> (0.0, 3.0] >> The smallest real number larger than 0.0 is its first point. > > You can repeat that as many times as you want, but that will not make > such a number to exist. > > 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: 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. He elaborates this understanding much more completely in his 9/16/2019 11:38 PM, reply. -- 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 | 2019-09-17 18:14 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <sv8gF.13475$DK.7459@fx21.fr7> |
| In reply to | #68473 |
On 17/09/2019 17:45, peteolcott wrote: > On 9/17/2019 3:05 AM, Juha Nieminen wrote: >> In comp.lang.c++ peteolcott <Here@home> wrote: >>> The length of this interval is exactly 3.0 >>> (0.0, 3.0] >>> The smallest real number larger than 0.0 is its first point. >> >> You can repeat that as many times as you want, but that will not make >> such a number to exist. >> >> 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: > > 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. > > He elaborates this understanding much more completely in his > 9/16/2019 11:38 PM, reply. The fact that this Keith Thompson bloke is also talking bollocks has no bearing on the fact that you are still hopelessly wrong. Do what someone else suggested and learn some number theory (and 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 | 2019-09-17 12:36 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <CYadneTrt-AOhBzAnZ2dnUU7-IfNnZ2d@giganews.com> |
| In reply to | #68475 |
On 9/17/2019 12:14 PM, Mr Flibble wrote: > On 17/09/2019 17:45, peteolcott wrote: >> On 9/17/2019 3:05 AM, Juha Nieminen wrote: >>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>> The length of this interval is exactly 3.0 >>>> (0.0, 3.0] >>>> The smallest real number larger than 0.0 is its first point. >>> >>> You can repeat that as many times as you want, but that will not make >>> such a number to exist. >>> >>> 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: >> >> 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. >> >> He elaborates this understanding much more completely in his >> 9/16/2019 11:38 PM, reply. > > The fact that this Keith Thompson bloke is also talking bollocks has no bearing on the fact that you are still hopelessly wrong. Do what someone else suggested and learn some number theory (and take your meds). > > /Flibble > Mike Terry also agrees with a key element. It is not that any of us are wrong. We would be wrong from the limited perspective of the Real number system, yet are not confined inside the box of this number system. When thinking outside the box occurs different number systems that are apparently more dense than the Real number system can be imagined. To people that are enclosed in the tight little boxes of conventional wisdom every new idea that contradicts their learned-by-rote seems to be an error. Recent research shows that inflexible thinking is due to abnormalities in the brain that show up on brain scans. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Mike Terry <news.dead.person.stones@darjeeling.plus.com> |
|---|---|
| Date | 2019-09-17 19:45 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <2YydncMPKI5UtBzAnZ2dnUU78VXNnZ2d@brightview.co.uk> |
| In reply to | #68476 |
On 17/09/2019 18:36, peteolcott wrote: > On 9/17/2019 12:14 PM, Mr Flibble wrote: >> On 17/09/2019 17:45, peteolcott wrote: >>> On 9/17/2019 3:05 AM, Juha Nieminen wrote: >>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>> The length of this interval is exactly 3.0 >>>>> (0.0, 3.0] >>>>> The smallest real number larger than 0.0 is its first point. >>>> >>>> You can repeat that as many times as you want, but that will not make >>>> such a number to exist. >>>> >>>> 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: >>> >>> 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. >>> >>> He elaborates this understanding much more completely in his >>> 9/16/2019 11:38 PM, reply. >> >> The fact that this Keith Thompson bloke is also talking bollocks has >> no bearing on the fact that you are still hopelessly wrong. Do what >> someone else suggested and learn some number theory (and take your meds). >> >> /Flibble >> > > Mike Terry also agrees with a key element. > It is not that any of us are wrong. We would be wrong from the limited > perspective of the Real number system, yet are not confined inside the > box of this number system. > > When thinking outside the box occurs different number systems that are > apparently more dense than the Real number system can be imagined. > > To people that are enclosed in the tight little boxes of conventional > wisdom every new idea that contradicts their learned-by-rote seems to > be an error. Recent research shows that inflexible thinking is due to > abnormalities in the brain that show up on brain scans. LOL, he's doing it to me now! (I don't think he knows I sometimes follow these newsgroups) For the record, I didn't say that PO wasn't wrong. In fact I can't see ANYTHING in the above paragraphs that matches up with ANYTHING I've said elsewhere. It's purely PO's words. PO believes he is an unacknowledged genius [ok, he said recently that /maybe/ he was only borderline genius - I don't want to give the impression PO is anything but modest!] but the truth is he's not a genius - he's actually a "DELUDED DUMBO". The DUMBO label comes from his inability to follow arguments and comprehend basic concepts in the fields he spouts forth his nonsense on. I'm sure he has previously tried to study at least a little CS and Logic, but he had to give up because it was all just beyond him. His knowledge of [everything] is just based on reading Wikipedia articles, without understanding them, and coming away with just a couple of keywords he can (mis)use. He admits to spending 15 years studying just two pages from a book (author Linz) covering the proof of the Halting Problem result. (And of course, he still doesn't get it...) The DELUDED label probably I don't need to explain further! Just in case it's not well known here: - he believes he is an unacknowledged (borderline) genius with powers beyond those of normal people - he is going to gain credibility as a logician/computer scientist/?? by refuting a string of key mathematical results that he does not even understand (Godel Incompleteness theorem, Halting Problem, Rice's theorem, Tarski's "undefineability of Truth", and lately "refuting Cardinality") - Then when he goes back to Doug Lenat (CYC project), Doug will have no choice but to put him in charge of the architecture for the Cyc upper ontology layer. - Then he will somehow become the first person to have created a "human mind inside a computer". - Umm, let's not get started on the "God beliefs" (He is God, the "actual creator of the universe", and he can make other individuals follow his will, just by wishing for them to do what he wants, and as God, he has access to a mode of infallible reasoning not available to others etc.. Hope I've got all that right!) Seriously, the God stuff is right out there - he even used this as a defense in a legal case in which he was involved: (Google "peter olcott god"). Normally I wouldn't bring that to anyone's attention, but hey, nobody likes cranks misusing their name for their own gain... Anyway, my suggestion is that if you want PO to keep on posting his OT rubbish in these newsgroups, keep on arguing with him to prove him wrong! He loves all that stuff. You certainly won't make him stop by nicely asking him not to post OT stuff... Mike.
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| From | Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> |
|---|---|
| Date | 2019-09-17 20:09 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <pbagF.13476$DK.7756@fx21.fr7> |
| In reply to | #68476 |
On 17/09/2019 18:36, peteolcott wrote: > On 9/17/2019 12:14 PM, Mr Flibble wrote: >> On 17/09/2019 17:45, peteolcott wrote: >>> On 9/17/2019 3:05 AM, Juha Nieminen wrote: >>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>> The length of this interval is exactly 3.0 >>>>> (0.0, 3.0] >>>>> The smallest real number larger than 0.0 is its first point. >>>> >>>> You can repeat that as many times as you want, but that will not make >>>> such a number to exist. >>>> >>>> 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: >>> >>> 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. >>> >>> He elaborates this understanding much more completely in his >>> 9/16/2019 11:38 PM, reply. >> >> The fact that this Keith Thompson bloke is also talking bollocks has no >> bearing on the fact that you are still hopelessly wrong. Do what someone >> else suggested and learn some number theory (and take your meds). >> >> /Flibble >> > > Mike Terry also agrees with a key element. > It is not that any of us are wrong. We would be wrong from the limited > perspective of the Real number system, yet are not confined inside the > box of this number system. > > When thinking outside the box occurs different number systems that are > apparently more dense than the Real number system can be imagined. > > To people that are enclosed in the tight little boxes of conventional > wisdom every new idea that contradicts their learned-by-rote seems to > be an error. Recent research shows that inflexible thinking is due to > abnormalities in the brain that show up on brain scans. You seriously need to take your meds, m8, you are quite mad. /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 | 2019-09-17 14:14 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <mPSdneABVvo7rRzAnZ2dnUU7-ePNnZ2d@giganews.com> |
| In reply to | #68482 |
On 9/17/2019 2:09 PM, Mr Flibble wrote: > On 17/09/2019 18:36, peteolcott wrote: >> On 9/17/2019 12:14 PM, Mr Flibble wrote: >>> On 17/09/2019 17:45, peteolcott wrote: >>>> On 9/17/2019 3:05 AM, Juha Nieminen wrote: >>>>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>>>> The length of this interval is exactly 3.0 >>>>>> (0.0, 3.0] >>>>>> The smallest real number larger than 0.0 is its first point. >>>>> >>>>> You can repeat that as many times as you want, but that will not make >>>>> such a number to exist. >>>>> >>>>> 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: >>>> >>>> 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. >>>> >>>> He elaborates this understanding much more completely in his >>>> 9/16/2019 11:38 PM, reply. >>> >>> The fact that this Keith Thompson bloke is also talking bollocks has no bearing on the fact that you are still hopelessly wrong. Do what someone else suggested and learn some number theory (and take your meds). >>> >>> /Flibble >>> >> >> Mike Terry also agrees with a key element. >> It is not that any of us are wrong. We would be wrong from the limited >> perspective of the Real number system, yet are not confined inside the >> box of this number system. >> >> When thinking outside the box occurs different number systems that are >> apparently more dense than the Real number system can be imagined. >> >> To people that are enclosed in the tight little boxes of conventional >> wisdom every new idea that contradicts their learned-by-rote seems to >> be an error. Recent research shows that inflexible thinking is due to >> abnormalities in the brain that show up on brain scans. > > You seriously need to take your meds, m8, you are quite mad. > > /Flibble > That you have totally run out of all reasoning as any rebuttal is sufficient evidence of the plausibility that my assertion is correct. You are very highly motivated to prove that I am wrong yet cannot only because I AM NOT WRONG !!! -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Mike Terry <news.dead.person.stones@darjeeling.plus.com> |
|---|---|
| Date | 2019-09-17 18:59 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <yaOdnXtHg6xjgxzAnZ2dnUU78UXNnZ2d@brightview.co.uk> |
| In reply to | #68475 |
On 17/09/2019 18:14, Mr Flibble wrote: > On 17/09/2019 17:45, peteolcott wrote: >> On 9/17/2019 3:05 AM, Juha Nieminen wrote: >>> In comp.lang.c++ peteolcott <Here@home> wrote: >>>> The length of this interval is exactly 3.0 >>>> (0.0, 3.0] >>>> The smallest real number larger than 0.0 is its first point. >>> >>> You can repeat that as many times as you want, but that will not make >>> such a number to exist. >>> >>> 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: >> >> 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. >> >> He elaborates this understanding much more completely in his >> 9/16/2019 11:38 PM, reply. > > The fact that this Keith Thompson bloke is also talking bollocks has no > bearing on the fact that you are still hopelessly wrong. Do what someone > else suggested and learn some number theory (and take your meds). > > /Flibble > Please do not assume that because PO says somebody or other "agrees" with him on something, that they actually do agree. And if they do agree ON SOME SPECIFIC POINT, within SOME QUALIFIED CONTEXT, that does not mean they "support" PO generally, or that PO has honestly represented their views with his selective quoting. For all you know, PO is quoting sentences you've written and presenting them elsewhere as "/Flibble over in xxxx agrees with me that xxxx", and people there are saying "Hey, that /Flibble guy doesn't half talk a load of bollocks!" Mike.
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| From | Keith Thompson <kst-u@mib.org> |
|---|---|
| Date | 2019-09-17 11:10 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <lnh85a94li.fsf@kst-u.example.com> |
| In reply to | #68473 |
peteolcott <Here@Home> writes:
> On 9/17/2019 3:05 AM, Juha Nieminen wrote:
>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>> The length of this interval is exactly 3.0
>>> (0.0, 3.0]
>>> The smallest real number larger than 0.0 is its first point.
>>
>> You can repeat that as many times as you want, but that will not make
>> such a number to exist.
>>
>> There is no "smallest real number larger than 0".
[...]
Agreed.
> Keith Thompson proves that he fully understands the Infinitesimal
> number system:
I do not fully understand infinitesimals, and I have not claimed
that I do.
[...]
--
Keith Thompson (The_Other_Keith) kst-u@mib.org <http://www.ghoti.net/~kst>
Will write code for food.
void Void(void) { Void(); } /* The recursive call of the void */
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 13:48 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <yo-dnUjEaOf-txzAnZ2dnUU7-fXNnZ2d@giganews.com> |
| In reply to | #68478 |
On 9/17/2019 1:10 PM, Keith Thompson wrote:
> peteolcott <Here@Home> writes:
>> On 9/17/2019 3:05 AM, Juha Nieminen wrote:
>>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>>> The length of this interval is exactly 3.0
>>>> (0.0, 3.0]
>>>> The smallest real number larger than 0.0 is its first point.
>>>
>>> You can repeat that as many times as you want, but that will not make
>>> such a number to exist.
>>>
>>> There is no "smallest real number larger than 0".
> [...]
>
> Agreed.
>
>> Keith Thompson proves that he fully understands the Infinitesimal
>> number system:
>
> I do not fully understand infinitesimals, and I have not claimed
> that I do.
This is the key essence of it:
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.
[A, B] - {A} = (A, B] encoded as [A[1], B[0]]
[A[1], B[0]] - {A[1]} = (A[1], B[0]] encoded as [A[2], B[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 | Keith Thompson <kst-u@mib.org> |
|---|---|
| Date | 2019-09-17 12:01 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <ln4l1a9276.fsf@kst-u.example.com> |
| In reply to | #68478 |
Keith Thompson <kst-u@mib.org> writes:
> peteolcott <Here@Home> writes:
[SNIP]
My apologies, I didn't notice which newsgroups this was posted to.
--
Keith Thompson (The_Other_Keith) kst-u@mib.org <http://www.ghoti.net/~kst>
Will write code for food.
void Void(void) { Void(); } /* The recursive call of the void */
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