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Groups > comp.lang.python > #65415 > unrolled thread
| Started by | Ayushi Dalmia <ayushidalmia2604@gmail.com> |
|---|---|
| First post | 2014-02-04 03:28 -0800 |
| Last post | 2014-02-05 15:22 +0000 |
| Articles | 20 on this page of 159 — 30 participants |
Back to article view | Back to comp.lang.python
Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 03:28 -0800
Re: Finding size of Variable Peter Otten <__peter__@web.de> - 2014-02-04 12:40 +0100
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 04:43 -0800
Re: Finding size of Variable Asaf Las <roegltd@gmail.com> - 2014-02-04 04:53 -0800
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 05:18 -0800
Re: Finding size of Variable Dave Angel <davea@davea.name> - 2014-02-04 08:09 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 05:19 -0800
Re: Finding size of Variable Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-02-04 09:06 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 21:00 -0800
Re:Finding size of Variable Dave Angel <davea@davea.name> - 2014-02-04 14:21 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 21:15 -0800
Re: Finding size of Variable Peter Otten <__peter__@web.de> - 2014-02-05 09:27 +0100
Re: Finding size of Variable Tim Golden <mail@timgolden.me.uk> - 2014-02-04 19:28 +0000
Re: Finding size of Variable Tim Chase <python.list@tim.thechases.com> - 2014-02-04 13:29 -0600
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 21:35 -0800
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-04 21:45 -0800
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-04 22:00 -0800
Re: Finding size of Variable Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-02-05 11:00 +0000
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-05 22:44 +1100
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-06 02:15 -0800
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-06 06:10 -0500
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-06 05:51 -0800
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-06 06:15 -0800
Re: Finding size of Variable Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-02-08 02:48 +0000
Re: Finding size of Variable Ethan Furman <ethan@stoneleaf.us> - 2014-02-07 19:02 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-08 13:17 +0000
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 17:45 -0500
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-08 17:25 -0800
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 21:56 -0500
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-09 13:59 +1100
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 22:07 -0500
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-08 22:09 -0500
Re: Finding size of Variable David Hutto <dwightdhutto@gmail.com> - 2014-02-08 22:09 -0500
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-08 22:16 -0500
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-08 19:30 -0800
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-10 06:07 -0800
Re: Finding size of Variable Asaf Las <roegltd@gmail.com> - 2014-02-10 06:25 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-10 14:39 +0000
Re: Finding size of Variable Tim Chase <python.list@tim.thechases.com> - 2014-02-10 08:43 -0600
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-11 10:53 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-11 19:04 +0000
Re: Finding size of Variable wxjmfauth@gmail.com - 2014-02-11 23:49 -0800
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-12 19:06 +1100
Re: Finding size of Variable Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2014-02-12 10:57 +0200
Re: Finding size of Variable Chris Angelico <rosuav@gmail.com> - 2014-02-12 20:24 +1100
Re: Finding size of Variable Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2014-02-12 11:35 +0200
Working with the set of real numbers (was: Finding size of Variable) Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 19:17 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) wxjmfauth@gmail.com - 2014-02-12 00:35 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) wxjmfauth@gmail.com - 2014-02-12 00:46 -0800
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 19:52 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Grant Edwards <invalid@invalid.invalid> - 2014-02-12 15:24 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) "Gisle Vanem" <gvanem@yahoo.no> - 2014-02-12 17:23 +0100
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-02-12 19:47 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2014-02-12 11:23 +0200
Re: Working with the set of real numbers (was: Finding size of Variable) albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-04 02:45 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-04 14:02 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Rustom Mody <rustompmody@gmail.com> - 2014-03-03 19:13 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-04 14:46 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Rustom Mody <rustompmody@gmail.com> - 2014-03-03 21:19 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-04 05:53 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-04 17:35 +1100
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-05 00:05 +1300
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-04 23:43 +1100
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-03-04 21:49 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 06:58 +1100
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 20:55 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-03-04 23:05 +0200
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 22:08 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 08:18 +1100
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 22:02 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 09:18 +1100
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-04 22:54 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-05 10:01 +1100
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-03-04 18:20 -0500
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-05 11:59 +0000
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-03-05 07:57 -0500
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-03-05 08:32 -0500
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-06 12:27 +0000
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-03-07 00:16 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-04 04:19 -0700
Re: Working with the set of real numbers (was: Finding size of Variable) albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-05 02:27 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-04 04:23 -0700
Re: Working with the set of real numbers (was: Finding size of Variable) albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-05 02:15 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-05 03:41 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Rustom Mody <rustompmody@gmail.com> - 2014-03-04 20:15 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Roy Smith <roy@panix.com> - 2014-03-04 23:25 -0500
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-03-05 15:37 +1100
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-03-04 20:57 -0800
Re: Working with the set of real numbers Roy Smith <roy@panix.com> - 2014-03-05 00:29 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-05 07:52 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve@pearwood.info> - 2014-03-05 08:38 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) wxjmfauth@gmail.com - 2014-03-05 01:00 -0800
Re: Working with the set of real numbers Ned Batchelder <ned@nedbatchelder.com> - 2014-03-05 06:23 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-05 12:21 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-05 17:43 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-06 05:01 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Kaynor <ckaynor@zindagigames.com> - 2014-03-05 10:03 -0800
Re: Working with the set of real numbers (was: Finding size of Variable) Grant Edwards <invalid@invalid.invalid> - 2014-03-05 19:13 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-03-05 21:22 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Roy Smith <roy@panix.com> - 2014-03-05 21:31 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-06 03:06 +0000
Re: Working with the set of real numbers (was: Finding size of Variable) Chris Angelico <rosuav@gmail.com> - 2014-03-06 14:14 +1100
Re: Working with the set of real numbers (was: Finding size of Variable) Roy Smith <roy@panix.com> - 2014-03-05 23:05 -0500
Re: Working with the set of real numbers (was: Finding size of Variable) Grant Edwards <invalid@invalid.invalid> - 2014-03-06 03:34 +0000
Re: Working with the set of real numbers Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-03-05 12:50 +0000
Re: Working with the set of real numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-05 17:49 +0000
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 19:56 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-12 20:16 +1100
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 21:07 +1100
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-02-12 06:11 -0800
Re: Working with the set of real numbers Ian Kelly <ian.g.kelly@gmail.com> - 2014-02-12 13:45 -0700
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-02-12 17:47 -0800
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-13 11:09 +1300
Re: Working with the set of real numbers Steven D'Aprano <steve@pearwood.info> - 2014-02-13 03:31 +0000
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-13 14:45 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-13 15:17 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-12 21:20 +1100
Re: Working with the set of real numbers wxjmfauth@gmail.com - 2014-02-12 02:55 -0800
Re: Working with the set of real numbers Ned Batchelder <ned@nedbatchelder.com> - 2014-02-12 06:55 -0500
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-12 14:48 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-13 00:20 +1100
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-12 16:13 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-13 04:52 +1100
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-13 11:24 +1300
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-02-12 17:56 -0500
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-14 18:26 +1300
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-12 22:44 +1100
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-12 22:58 +1100
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-13 11:32 +1300
Re: Working with the set of real numbers Grant Edwards <invalid@invalid.invalid> - 2014-02-12 23:23 +0000
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-12 14:04 +0000
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-12 06:14 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-12 14:25 +0000
Re: Finding size of Variable Rustom Mody <rustompmody@gmail.com> - 2014-02-12 06:32 -0800
Re: Working with the set of real numbers Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2014-02-13 12:48 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-13 16:00 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-14 06:25 +1100
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-13 21:47 +0200
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-14 07:08 +1100
Re: Working with the set of real numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2014-02-13 22:05 -0800
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-15 00:30 +1300
Re: Working with the set of real numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2014-02-14 16:26 -0800
Re: Working with the set of real numbers albert@spenarnc.xs4all.nl (Albert van der Horst) - 2014-03-05 02:38 +0000
Re: Working with the set of real numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-02-14 19:37 +1300
Re: Working with the set of real numbers Chris Angelico <rosuav@gmail.com> - 2014-02-14 17:44 +1100
Re: Working with the set of real numbers Rustom Mody <rustompmody@gmail.com> - 2014-02-14 07:13 -0800
Re: Working with the set of real numbers Dave Angel <davea@davea.name> - 2014-02-14 07:30 -0500
Re: Working with the set of real numbers Grant Edwards <invalid@invalid.invalid> - 2014-02-14 15:09 +0000
Re: Working with the set of real numbers Rotwang <sg552@hotmail.co.uk> - 2014-02-13 21:29 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-14 00:00 +0200
Re: Working with the set of real numbers Rotwang <sg552@hotmail.co.uk> - 2014-02-13 22:21 +0000
Re: Working with the set of real numbers Marko Rauhamaa <marko@pacujo.net> - 2014-02-14 01:16 +0200
Re: Working with the set of real numbers Ben Finney <ben+python@benfinney.id.au> - 2014-02-14 03:57 +1100
Re: Finding size of Variable Ned Batchelder <ned@nedbatchelder.com> - 2014-02-10 10:02 -0500
Re: Finding size of Variable Neil Cerutti <neilc@norwich.edu> - 2014-02-11 14:29 +0000
Re: Finding size of Variable Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-02-05 22:14 -0500
Re: Finding size of Variable Dave Angel <davea@davea.name> - 2014-02-05 08:43 -0500
Re: Finding size of Variable Ayushi Dalmia <ayushidalmia2604@gmail.com> - 2014-02-05 06:33 -0800
Re: Finding size of Variable Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-02-05 15:22 +0000
Page 6 of 8 — ← Prev page 1 2 3 4 5 [6] 7 8 Next page →
| From | Steven D'Aprano <steve+comp.lang.python@pearwood.info> |
|---|---|
| Date | 2014-03-06 03:06 +0000 |
| Subject | Re: Working with the set of real numbers (was: Finding size of Variable) |
| Message-ID | <5317e640$0$29985$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #67910 |
On Wed, 05 Mar 2014 21:31:51 -0500, Roy Smith wrote: > In article <53176225$0$29987$c3e8da3$5496439d@news.astraweb.com>, > Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote: > >> Physics is the fundamental science, at least according to the >> physicists, and Real Soon Now they'll have a Theory Of Everything, >> something small enough to print on a tee-shirt, which will explain >> everything. At least in principle. > > A mathematician, a chemist, and a physicist are arguing the nature of > prime numbers. The chemist says, "All odd numbers are prime. Look, I > can prove it. Three is prime. Five is prime. Seven is prime". The > mathematician says, "That's nonsense. Nine is not prime". The > physicist looks at him and says, "Hmmmm, you may be right, but eleven is > prime, and thirteen is prime. It appears that within the limits of > experimental error, all odd number are indeed prime!" They ask a computer programmer to adjudicate who is right, so he writes a program to print out all the primes: 1 is prime 1 is prime 1 is prime 1 is prime 1 is prime ... -- Steven D'Aprano http://import-that.dreamwidth.org/
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| From | Chris Angelico <rosuav@gmail.com> |
|---|---|
| Date | 2014-03-06 14:14 +1100 |
| Subject | Re: Working with the set of real numbers (was: Finding size of Variable) |
| Message-ID | <mailman.7858.1394075692.18130.python-list@python.org> |
| In reply to | #67914 |
On Thu, Mar 6, 2014 at 2:06 PM, Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote: > They ask a computer programmer to adjudicate who is right, so he writes a > program to print out all the primes: > > 1 is prime > 1 is prime > 1 is prime > 1 is prime > 1 is prime And he claimed that he was correct, because he had - as is known to be true in reality - a countably infinite number of primes. ChrisA
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| From | Roy Smith <roy@panix.com> |
|---|---|
| Date | 2014-03-05 23:05 -0500 |
| Subject | Re: Working with the set of real numbers (was: Finding size of Variable) |
| Message-ID | <roy-80F6FB.23050205032014@news.panix.com> |
| In reply to | #67914 |
In article <5317e640$0$29985$c3e8da3$5496439d@news.astraweb.com>, Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote: > On Wed, 05 Mar 2014 21:31:51 -0500, Roy Smith wrote: > > > In article <53176225$0$29987$c3e8da3$5496439d@news.astraweb.com>, > > Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote: > > > >> Physics is the fundamental science, at least according to the > >> physicists, and Real Soon Now they'll have a Theory Of Everything, > >> something small enough to print on a tee-shirt, which will explain > >> everything. At least in principle. > > > > A mathematician, a chemist, and a physicist are arguing the nature of > > prime numbers. The chemist says, "All odd numbers are prime. Look, I > > can prove it. Three is prime. Five is prime. Seven is prime". The > > mathematician says, "That's nonsense. Nine is not prime". The > > physicist looks at him and says, "Hmmmm, you may be right, but eleven is > > prime, and thirteen is prime. It appears that within the limits of > > experimental error, all odd number are indeed prime!" > > They ask a computer programmer to adjudicate who is right, so he writes a > program to print out all the primes: > > 1 is prime > 1 is prime > 1 is prime > 1 is prime > 1 is prime > ... So, a mathematician, a biologist, and a physicist are watching a house. The physicist says, "It appears to be empty". Sometime later, a man and a woman go into the house. Shortly after that, the man and the woman come back out, with a child. The biologist says, "They must have reproduced". The mathematician says, "If one more person goes into the house, it'll be empty again".
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| From | Grant Edwards <invalid@invalid.invalid> |
|---|---|
| Date | 2014-03-06 03:34 +0000 |
| Subject | Re: Working with the set of real numbers (was: Finding size of Variable) |
| Message-ID | <lf8qbi$5v$1@reader1.panix.com> |
| In reply to | #67910 |
On 2014-03-06, Roy Smith <roy@panix.com> wrote: > In article <53176225$0$29987$c3e8da3$5496439d@news.astraweb.com>, > Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote: > >> Physics is the fundamental science, at least according to the >> physicists, and Real Soon Now they'll have a Theory Of Everything, >> something small enough to print on a tee-shirt, which will explain >> everything. At least in principle. > > A mathematician, a chemist, and a physicist are arguing the nature of > prime numbers. The chemist says, "All odd numbers are prime. Look, I > can prove it. Three is prime. Five is prime. Seven is prime". The > mathematician says, "That's nonsense. Nine is not prime". The > physicist looks at him and says, "Hmmmm, you may be right, but eleven > is prime, and thirteen is prime. It appears that within the limits of > experimental error, all odd number are indeed prime!" Assuming spherical odd numbers in a vacuum on a frictionless surface, of course. -- Grant
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| From | Mark Lawrence <breamoreboy@yahoo.co.uk> |
|---|---|
| Date | 2014-03-05 12:50 +0000 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.7819.1394023826.18130.python-list@python.org> |
| In reply to | #67820 |
On 05/03/2014 12:21, Oscar Benjamin wrote: > > Why the dig at physicists? I think most physicists would be able to > tell you that the sum of all natural numbers is not -1/12. In fact > most people with very little background in mathematics can tell you > that. > I'll put that one to the test tomorrow morning when the bin men come round. I fully expect them to dial 999 and ask that the paramedics are armed with plenty of sedatives. -- My fellow Pythonistas, ask not what our language can do for you, ask what you can do for our language. Mark Lawrence --- This email is free from viruses and malware because avast! Antivirus protection is active. http://www.avast.com
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| From | Steven D'Aprano <steve+comp.lang.python@pearwood.info> |
|---|---|
| Date | 2014-03-05 17:49 +0000 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <531763ab$0$29985$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #67843 |
On Wed, 05 Mar 2014 12:50:06 +0000, Mark Lawrence wrote: > On 05/03/2014 12:21, Oscar Benjamin wrote: >> >> Why the dig at physicists? I think most physicists would be able to >> tell you that the sum of all natural numbers is not -1/12. In fact most >> people with very little background in mathematics can tell you that. >> >> > I'll put that one to the test tomorrow morning when the bin men come > round. Do you seriously think that garbos (bin men) know more about mathematics than mathematicians? > I fully expect them to dial 999 and ask that the paramedics are > armed with plenty of sedatives. You know that rather large piece of machinery in Europe called the Large Hadron Collider? The one which is generating some rather extraordinary proofs of fundamental physics, such as the Higgs Boson? A lot of that physics is based on theory which uses the same logic and mathematics that you are mocking. Laugh away, but the universe behaves as if the sum of the natural numbers is -1/12. -- Steven D'Aprano http://import-that.dreamwidth.org/
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| From | Ben Finney <ben+python@benfinney.id.au> |
|---|---|
| Date | 2014-02-12 19:56 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6739.1392195606.18130.python-list@python.org> |
| In reply to | #66004 |
Chris Angelico <rosuav@gmail.com> writes: > On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney <ben+python@benfinney.id.au> wrote: > > Chris Angelico <rosuav@gmail.com> writes: > > > >> I have yet to find any computer that works with the set of real > >> numbers in any way. Never mind optimization, they simply cannot > >> work with real numbers. > > > > Not *any* computer? Not in *any* way? The Python built-in ‘float’ > > type “works with the set of real numbers”, in a way. > > No, the Python built-in float type works with a subset of real numbers So, “works with a subset of real numbers” is not satisfactory, then. Okay. > Same goes for fractions.Fraction and [c]decimal.Decimal. All of them > are restricted to some subset of rational numbers, not all reals. > > > What specific behaviour would, for you, qualify as “works with the > > set of real numbers in any way”? > > Being able to represent surds, pi, e, etc, for a start. So, if I understand you right, you want to say that you've not found a computer that works with the *complete* set of real numbers. Yes? -- \ “To have the choice between proprietary software packages, is | `\ being able to choose your master. Freedom means not having a | _o__) master.” —Richard M. Stallman, 2007-05-16 | Ben Finney
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| From | Chris Angelico <rosuav@gmail.com> |
|---|---|
| Date | 2014-02-12 20:16 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6740.1392196605.18130.python-list@python.org> |
| In reply to | #66004 |
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney <ben+python@benfinney.id.au> wrote: > So, if I understand you right, you want to say that you've not found a > computer that works with the *complete* set of real numbers. Yes? Correct. When jmf referred to real numbers, he implied that there are no optimizations done for natural numbers, that everything's just as efficient for any real number as for any other. My point is that computers *do not* work with real numbers, but only ever with some subset thereof, and that certain subsets (integers usually) are optimized for in ways that other subsets aren't. A true "real number" type might be useful in a few extremely narrow situations, but for the most part, I'd much rather have the optimized implementation that works with a subset thereof, and actually runs within reasonable time/space complexity. (Though, that said, I think a lot of programmers could do with some education on exactly _what_ subset of real numbers they're working with. The classic IEEE double-precision floating point type is good enough with low numbers that lots of people seem to think it stores reals, which it doesn't.) ChrisA
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| From | Ben Finney <ben+python@benfinney.id.au> |
|---|---|
| Date | 2014-02-12 21:07 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6749.1392199638.18130.python-list@python.org> |
| In reply to | #66004 |
Chris Angelico <rosuav@gmail.com> writes: > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney <ben+python@benfinney.id.au> wrote: > > So, if I understand you right, you want to say that you've not found > > a computer that works with the *complete* set of real numbers. Yes? > > Correct. […] My point is that computers *do not* work with real > numbers, but only ever with some subset thereof […] You've done it again: by saying that “computers *do not* work with real numbers”, that if I find a real number – e.g. the number 4 – your position is that, since it's a real number, computers don't work with that number. That's why I think you need to be clear that your point isn't “computers don't work with real numbers”, but rather “computers work only with a limited subset of real numbers”. -- \ “We have to go forth and crush every world view that doesn't | `\ believe in tolerance and free speech.” —David Brin | _o__) | Ben Finney
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| From | Rustom Mody <rustompmody@gmail.com> |
|---|---|
| Date | 2014-02-12 06:11 -0800 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <10afc311-f907-4eb8-859e-99180d1c07c0@googlegroups.com> |
| In reply to | #66023 |
On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote: > Chris Angelico writes: > > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote: > > > So, if I understand you right, you want to say that you've not found > > > a computer that works with the *complete* set of real numbers. Yes? > > Correct. [...] My point is that computers *do not* work with real > > numbers, but only ever with some subset thereof [...] > You've done it again: by saying that "computers *do not* work with real > numbers", that if I find a real number - e.g. the number 4 - your > position is that, since it's a real number, computers don't work with > that number. There is a convention in logic called the implicit universal quantifier convention: when a bald unqualified reference is in a statement it means it is universally quantified. eg "A triangle is a polygon with 3 sides" really means "ALL polygons with 3 sides are triangles" ie the ALL is implied Now when for-all is inverted by de Morgan it becomes "for-some not..." So "computers work with real numbers" really means "computers work with all real numbers" and that is not true > That's why I think you need to be clear that your point isn't "computers > don't work with real numbers", but rather "computers work only with a > limited subset of real numbers". Yes both these statements are true by above. In fact computers cannot work with real numbers because the real number set is undecidable/uncomputable. In particular, trivial operations like equality on reals -- IN GENERAL -- is undecidable.
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| From | Ian Kelly <ian.g.kelly@gmail.com> |
|---|---|
| Date | 2014-02-12 13:45 -0700 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6781.1392237972.18130.python-list@python.org> |
| In reply to | #66037 |
On Wed, Feb 12, 2014 at 7:11 AM, Rustom Mody <rustompmody@gmail.com> wrote: > On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote: >> Chris Angelico writes: > >> > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote: >> > > So, if I understand you right, you want to say that you've not found >> > > a computer that works with the *complete* set of real numbers. Yes? >> > Correct. [...] My point is that computers *do not* work with real >> > numbers, but only ever with some subset thereof [...] > >> You've done it again: by saying that "computers *do not* work with real >> numbers", that if I find a real number - e.g. the number 4 - your >> position is that, since it's a real number, computers don't work with >> that number. > > There is a convention in logic called the implicit universal quantifier > convention: when a bald unqualified reference is in a statement it means > it is universally quantified. eg > "A triangle is a polygon with 3 sides" > really means > "ALL polygons with 3 sides are triangles" ie the ALL is implied > > Now when for-all is inverted by de Morgan it becomes "for-some not..." > > So "computers work with real numbers" really means "computers work with > all real numbers" and that is not true I take exception whenever I see somebody trying to use predicate logic to determine the meaning of an English sentence. English does not follow the rules of predicate logic, and English sentences do not map consistently to logical sentences. To me, the meaning of "computers do not work with X" depends upon the domain of X. "Computers do not work with real numbers" implies that computers do not work with the set of real numbers (but implies nothing about subsets). "Computers do not work with keyboards" on the other hand would imply that no computer works with any keyboard (which of course is demonstrably false).
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| From | Rustom Mody <rustompmody@gmail.com> |
|---|---|
| Date | 2014-02-12 17:47 -0800 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <4ee92a2b-41ec-4b8b-b1fe-bfea15166487@googlegroups.com> |
| In reply to | #66082 |
On Thursday, February 13, 2014 2:15:28 AM UTC+5:30, Ian wrote: > On Wed, Feb 12, 2014 at 7:11 AM, Rustom Mody wrote: > > On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote: > >> Chris Angelico writes: > >> > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote: > >> > > So, if I understand you right, you want to say that you've not found > >> > > a computer that works with the *complete* set of real numbers. Yes? > >> > Correct. [...] My point is that computers *do not* work with real > >> > numbers, but only ever with some subset thereof [...] > >> You've done it again: by saying that "computers *do not* work with real > >> numbers", that if I find a real number - e.g. the number 4 - your > >> position is that, since it's a real number, computers don't work with > >> that number. > > There is a convention in logic called the implicit universal quantifier > > convention: when a bald unqualified reference is in a statement it means > > it is universally quantified. eg > > "A triangle is a polygon with 3 sides" > > really means > > "ALL polygons with 3 sides are triangles" ie the ALL is implied > > Now when for-all is inverted by de Morgan it becomes "for-some not..." > > So "computers work with real numbers" really means "computers work with > > all real numbers" and that is not true > I take exception whenever I see somebody trying to use predicate logic > to determine the meaning of an English sentence. Ok See below. > English does not follow the rules of predicate logic, Agreed > and English sentences do not map consistently to logical sentences. Agreed > To me, the meaning of "computers do not work with X" depends upon the > domain of X. Agreed > "Computers do not work with real numbers" implies that > computers do not work with the set of real numbers (but implies > nothing about subsets). How come? > "Computers do not work with keyboards" on the > other hand would imply that no computer works with any keyboard (which > of course is demonstrably false). The example is the other way. If one says: "Computers have keyboards" and then we have the demonstratation of say - a cloud server - a android phone which are computers that have no keyboards, then that demonstrates that "(ALL) computers have keyboards" is false" Two things therefore come into play here: 1. "All computers have keyboards" is falsified by predicate logic 2. Modelling the English "Computers have keyboards" to the above sentence needs: grammar, context, good-sense, good-will and a lot of other good (and soft) stuff. tl;dr Predicate logic can help to gain some clarity about where the implied but unstated quantifiers lie.
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| From | Gregory Ewing <greg.ewing@canterbury.ac.nz> |
|---|---|
| Date | 2014-02-13 11:09 +1300 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <bm29pnF4iqtU1@mid.individual.net> |
| In reply to | #66023 |
Ben Finney wrote: > That's why I think you need to be clear that your point isn't “computers > don't work with real numbers”, but rather “computers work only with a > limited subset of real numbers”. They actually work with a subset of *rational* numbers. All floats representable by a computer are rational. The rationals happen to be a subset of the reals, but that's kind of beside the point given that a float can't represent *any* real number that isn't also a rational. -- Greg
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| From | Steven D'Aprano <steve@pearwood.info> |
|---|---|
| Date | 2014-02-13 03:31 +0000 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <52fc3c7c$0$11128$c3e8da3@news.astraweb.com> |
| In reply to | #66023 |
On Wed, 12 Feb 2014 21:07:04 +1100, Ben Finney wrote:
> Chris Angelico <rosuav@gmail.com> writes:
>
>> On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney
>> <ben+python@benfinney.id.au> wrote:
>> > So, if I understand you right, you want to say that you've not found
>> > a computer that works with the *complete* set of real numbers. Yes?
>>
>> Correct. […] My point is that computers *do not* work with real
>> numbers, but only ever with some subset thereof […]
>
> You've done it again: by saying that “computers *do not* work with real
> numbers”, that if I find a real number – e.g. the number 4 – your
> position is that, since it's a real number, computers don't work with
> that number.
That answer relies on the assumption that "computers do not work with X"
implies:
for each element x in X:
it is true that "computers do not work with x"
that is to say, a single counter-example of computers working with an
element of X, even if it is a fluke, is enough to disprove the rule.
To give a real-world, non-programming example:
"The former South African apartheid government did not respect the
Universal Human Rights of blacks."
Under your strict interpretation, we would have to say that even a single
example of the apartheid government respecting even a single human rights
of a single black person would be sufficient to disprove the claim.
But there's another interpretation available to us, one which is more
suited to natural language statements as made by Chris: we interpret
"computers do not work with X" as meaning:
there is at least one element x, such that it is true that
"computers do not work with x"
In the case of real numbers, there is an *uncountably infinite* number of
such elements x. In fact, we can pick any two distinct numbers, no matter
how close together, say:
1
1.000000000001
and be sure that there are an uncountably infinite number of real numbers
which computers do not work with between those two values.
For the record, "uncountable infinite" is not just me emphasising that
infinity is too big to count. It's a technical term from mathematics. In
a nutshell it means that not only are there too many elements to count,
but even in an infinite amount of time you couldn't count them all, not
even if you counted infinitely fast.
In fact, it isn't just that there are *specific* real numbers which
computers cannot represent (say, irrationals like pi or e, really tiny
numbers like 1/(googleplex**googleplex**googleplex), or really huge ones
like Graham's Number), but that the fundamental mathematical laws of the
reals are violated by computers.
For example, it is not true that for every number x, 1/1(x)) == x.
py> 1/(1/93.0) == 93.0
False
Nor is it always true that a*(b+c) equals a*b + a*c, or that a+b+c is
necessarily equal to b+c+a.
So it isn't even that floats are merely a subset of reals. They're
actually not reals at all, since the fundamental properties of real
numbers do not always apply to floating point calculations.
--
Steven
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| From | Ben Finney <ben+python@benfinney.id.au> |
|---|---|
| Date | 2014-02-13 14:45 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6820.1392263134.18130.python-list@python.org> |
| In reply to | #66145 |
Steven D'Aprano <steve@pearwood.info> writes: > On Wed, 12 Feb 2014 21:07:04 +1100, Ben Finney wrote: > > > You've done it again: by saying that “computers *do not* work with > > real numbers”, that if I find a real number – e.g. the number 4 – > > your position is that, since it's a real number, computers don't > > work with that number. > > That answer relies on the assumption that "computers do not work with X" > implies: > > for each element x in X: > it is true that "computers do not work with x" > > that is to say, a single counter-example of computers working with an > element of X, even if it is a fluke, is enough to disprove the rule. Right. I'm pointing out that this is a natural interpretation of “computers do not work with X”. That is not the *only* natural interpretation, of course. But it is IMO a common enough interpretation that when trying to communicate clearly, one should re-phrase to avoid that false implication. -- \ “I prayed for twenty years but received no answer until I | `\ prayed with my legs.” —Frederick Douglass, escaped slave | _o__) | Ben Finney
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| From | Chris Angelico <rosuav@gmail.com> |
|---|---|
| Date | 2014-02-13 15:17 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6823.1392265065.18130.python-list@python.org> |
| In reply to | #66145 |
On Thu, Feb 13, 2014 at 2:31 PM, Steven D'Aprano <steve@pearwood.info> wrote: > "The former South African apartheid government did not respect the > Universal Human Rights of blacks." > > Under your strict interpretation, we would have to say that even a single > example of the apartheid government respecting even a single human rights > of a single black person would be sufficient to disprove the claim. Right. A common interpretation of that statement would be that, by and large, one can see a parallel between "people whose rights are not respected" and "people with black skin". The existence of a single black person whose rights are respected, or a single non-black person whose rights are not respected, doesn't change that; if there are X million black people whose rights are not respected, and Y million white people who are treated like people, and the converses are measured in thousands, then the statement would be considered valid. (That said, though, if there *were* a black person whose rights were respected, then it would be highly notable. I don't know if there had been such a case with .za, but there were - if you'll forgive me for Godwinning - a very VERY small number of Jews who held high position in Nazi Germany, and who were not harmed because they were of too great value to lose. It's notable because respecting a single person of a category of people considered "sub-human" effectively disproves the notion that "all X are less than people". (If one Jew is worth keeping around, how can you say that Jews are, by definition, subhuman? If one black woman can hold a highly respected position in a university, doesn't that prove that black people and women are just as intelligent as white males?) But, notable or not, it doesn't change the fact that Nazi Germany *as a whole* considered Jews *as a group* to be insignificant, and that the apartheid .za govt treated black-skinned people *as a group* to be insignificant.) So where does that leave computers and reals? Well, it comes down to descriptors. Suppose there were a place where all people are treated perfectly fairly, UNLESS a white-skinned person is male and aged between 13 and 20, in which case he is considered guilty until proven innocent. Does this place treat males and females equally? Not really. But it's also not really accurate to say that "men are mistreated by the law", any more than it's accurate to say that "IEEE floating point handles real numbers". I certainly would not say that an integer type "works with real numbers", simply because it's almost completely useless to say that - since it's such a tight subset of them. ChrisA
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| From | Chris Angelico <rosuav@gmail.com> |
|---|---|
| Date | 2014-02-12 21:20 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6751.1392200425.18130.python-list@python.org> |
| In reply to | #66004 |
On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney <ben+python@benfinney.id.au> wrote: > Chris Angelico <rosuav@gmail.com> writes: > >> On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney <ben+python@benfinney.id.au> wrote: >> > So, if I understand you right, you want to say that you've not found >> > a computer that works with the *complete* set of real numbers. Yes? >> >> Correct. […] My point is that computers *do not* work with real >> numbers, but only ever with some subset thereof […] > > You've done it again: by saying that “computers *do not* work with real > numbers”, that if I find a real number – e.g. the number 4 – your > position is that, since it's a real number, computers don't work with > that number. > > That's why I think you need to be clear that your point isn't “computers > don't work with real numbers”, but rather “computers work only with a > limited subset of real numbers”. Hmm, I'm not sure that my statement is false. If a computer can work with "real numbers", then I would expect it to be able to work with any real number. In C, I can declare an 'int' variable, which can hold the real number 4 - does that mean that that variable stores real numbers? No, and it's not useful to say that it does. It doesn't store rationals either, even though 4 is a rational. The fact that computers can work with some subset of real numbers does not disprove my statement that computers don't work with "real numbers" as a class. Program X works with text files, but it fails if the file contains U+003C; can I feed it this thing, which is a text file? No, I can't, because it works only with a subset of text files. ChrisA
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| From | wxjmfauth@gmail.com |
|---|---|
| Date | 2014-02-12 02:55 -0800 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <ed1046c9-9fb1-4f0c-a338-0af6abe473eb@googlegroups.com> |
| In reply to | #66025 |
The fascinating aspect of this FSR lies in its mathematical absurdity. jmf
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| From | Ned Batchelder <ned@nedbatchelder.com> |
|---|---|
| Date | 2014-02-12 06:55 -0500 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6753.1392206171.18130.python-list@python.org> |
| In reply to | #66027 |
On 2/12/14 5:55 AM, wxjmfauth@gmail.com wrote: > The fascinating aspect of this FSR lies > in its mathematical absurdity. > > jmf > Stop. -- Ned Batchelder, http://nedbatchelder.com
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| From | Marko Rauhamaa <marko@pacujo.net> |
|---|---|
| Date | 2014-02-12 14:48 +0200 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <8761okcx8z.fsf@elektro.pacujo.net> |
| In reply to | #66025 |
Chris Angelico <rosuav@gmail.com>: > Hmm, I'm not sure that my statement is false. If a computer can work > with "real numbers", then I would expect it to be able to work with > any real number. In C, I can declare an 'int' variable, which can hold > the real number 4 - does that mean that that variable stores real > numbers? No, and it's not useful to say that it does. It doesn't store > rationals either, even though 4 is a rational. The fact that computers > can work with some subset of real numbers does not disprove my > statement that computers don't work with "real numbers" as a class. > Program X works with text files, but it fails if the file contains > U+003C; can I feed it this thing, which is a text file? No, I can't, > because it works only with a subset of text files. According to your definition, there's no computer in the world that can work with integers or text files. Marko
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