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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 | 19 on this page of 159 — 30 participants |
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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 8 of 8 — ← Prev page 1 2 3 4 5 6 7 [8]
| From | Gregory Ewing <greg.ewing@canterbury.ac.nz> |
|---|---|
| Date | 2014-02-15 00:30 +1300 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <bm6d29F924U1@mid.individual.net> |
| In reply to | #66284 |
Devin Jeanpierre wrote: > There is no way to iterate over all the reals one at a time, no matter > how fast you execute instructions. If you could, it would be trivial > to show that the reals have the same cardinality as the positive > integers: correspond n with the whatever is returned by the nth call > to it.next. You're assuming that the calls to it.next are discrete events separated by some nonzero time interval. A decent transfinite processor would make a continuum of calls, and execute uncountably many of them in any finite period of time. -- Greg
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| From | Devin Jeanpierre <jeanpierreda@gmail.com> |
|---|---|
| Date | 2014-02-14 16:26 -0800 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6946.1392424026.18130.python-list@python.org> |
| In reply to | #66291 |
On Fri, Feb 14, 2014 at 3:30 AM, Gregory Ewing <greg.ewing@canterbury.ac.nz> wrote: > Devin Jeanpierre wrote: >> There is no way to iterate over all the reals one at a time, no matter >> how fast you execute instructions. If you could, it would be trivial >> to show that the reals have the same cardinality as the positive >> integers: correspond n with the whatever is returned by the nth call >> to it.next. > > > You're assuming that the calls to it.next are discrete > events separated by some nonzero time interval. I'm not. If you want to imagine infinitely fast computers, you must allow for things to "precede" each other in the program's execution, or else you can't execute any program at all. In such an infinitely fast computer, if iteration works by calling a .next() method repeatedly, it can't iterate uncountably many times, by construction. If you're executing uncountably many instructions per second, the loop would terminate immediately, having executed countably infinitely many iterations. > A decent transfinite processor would make a continuum > of calls, and execute uncountably many of them in any > finite period of time. Yes, you could imagine a computer that does a thing for every real. My issue is that the cited thing is transfinite induction, for which the induction covers countably many values; handling of the rest of the values is a second step. This is also the implication of such a word as "iteration". I suppose this was accidental on the part of the poster, and I shouldn't have disagreed so strongly. I suspect they meant what you are getting at, instead, which is that there is no successor to any iteration, and between any two iterations there are uncountably many iterations that happened. Operations occur in an order, but not sequentially. (Of course, such a machine would be alien and absurd.) -- Devin
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| From | albert@spenarnc.xs4all.nl (Albert van der Horst) |
|---|---|
| Date | 2014-03-05 02:38 +0000 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <53168e1a$0$25064$e4fe514c@dreader37.news.xs4all.nl> |
| In reply to | #66220 |
In article <87fvnm7q1n.fsf@elektro.pacujo.net>, Marko Rauhamaa <marko@pacujo.net> wrote: >Chris Angelico <rosuav@gmail.com>: > >> On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa <marko@pacujo.net> wrote: >>> Well, if your idealized, infinite, digital computer had ℵ₁ bytes of RAM >>> and ran at ℵ₁ hertz and Python supported transfinite iteration, you >>> could easily do reals: >>> >>> for x in continuum(0, max(1, y)): >> >> How exactly do you iterate over a continuum, with a digital computer? > >How "digital" our idealized computers are is a matter for a debate. >However, iterating over the continuum is provably "possible:" > > http://en.wikipedia.org/wiki/Transfinite_induction > >> it would take a finite amount of time to assign to x the "next >> number", ergo your algorithm can't guarantee to finish in finite time. > >My assumption was you could execute ℵ₁ statements per second. That >doesn't guarantee a finite finish time but would make it possible. That >is because > > ℵ₁ * ℵ₁ = ℵ₁ = ℵ₁ * 1 > >This computer is definitely more powerful than a Turing machine, which >only has ℵ₀ bytes of RAM and thus can't even store an arbitrary real >value in memory. You're very much off the track here. A Turing machine is an abstraction for a computer were the limitations of size are gone. The most obvious feature of a Turing machine is an infinite tape. A Turing machine happily calculates Ackerman functions long after a real machine runs out of memory to represent it, with as a result a number of ones on that tape. But it only happens in the mathematicians mind. > > >Marko -- Albert van der Horst, UTRECHT,THE NETHERLANDS Economic growth -- being exponential -- ultimately falters. albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst
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| From | Gregory Ewing <greg.ewing@canterbury.ac.nz> |
|---|---|
| Date | 2014-02-14 19:37 +1300 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <bm5rspFr2l7U1@mid.individual.net> |
| In reply to | #66213 |
Chris Angelico wrote: > Even adding to your requirements that it have an ℵ₁ Hz bus (which, by > the way, I *totally* want - the uses are endless), it would take a > finite amount of time to assign to x the "next number", ergo your > algorithm can't guarantee to finish in finite time. If it's a quantum computer, it may be able to execute all branches of the iteration in parallel. But it would only have a probability of returning the right answer (in other cases it would kill your cat). -- Greg
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| From | Chris Angelico <rosuav@gmail.com> |
|---|---|
| Date | 2014-02-14 17:44 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6909.1392360280.18130.python-list@python.org> |
| In reply to | #66285 |
On Fri, Feb 14, 2014 at 5:37 PM, Gregory Ewing <greg.ewing@canterbury.ac.nz> wrote: > Chris Angelico wrote: >> >> Even adding to your requirements that it have an ℵ₁ Hz bus (which, by >> the way, I *totally* want - the uses are endless), it would take a >> >> finite amount of time to assign to x the "next number", ergo your >> algorithm can't guarantee to finish in finite time. > > > If it's a quantum computer, it may be able to execute > all branches of the iteration in parallel. But it > would only have a probability of returning the right > answer (in other cases it would kill your cat). Oh, that's fine, he's not my cat anyway. Go ahead, build it. ChrisA
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| From | Rustom Mody <rustompmody@gmail.com> |
|---|---|
| Date | 2014-02-14 07:13 -0800 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <09f907b2-dba0-4b5d-8387-1f8ea453d020@googlegroups.com> |
| In reply to | #66286 |
On Friday, February 14, 2014 12:14:31 PM UTC+5:30, Chris Angelico wrote: > Oh, that's fine, he's not my cat anyway. Go ahead, build it. Now Now! I figured you were the cat out here!
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| From | Dave Angel <davea@davea.name> |
|---|---|
| Date | 2014-02-14 07:30 -0500 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6915.1392380812.18130.python-list@python.org> |
| In reply to | #66285 |
Chris Angelico <rosuav@gmail.com> Wrote in message: > On Fri, Feb 14, 2014 at 5:37 PM, Gregory Ewing >> >> >> If it's a quantum computer, it may be able to execute >> all branches of the iteration in parallel. But it >> would only have a probability of returning the right >> answer (in other cases it would kill your cat). > > Oh, that's fine, he's not my cat anyway. Go ahead, build it. > That cat has got to be at least 79 by now. Probably starved by now. -- DaveA
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| From | Grant Edwards <invalid@invalid.invalid> |
|---|---|
| Date | 2014-02-14 15:09 +0000 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <ldlbiu$2dk$1@reader1.panix.com> |
| In reply to | #66285 |
On 2014-02-14, Gregory Ewing <greg.ewing@canterbury.ac.nz> wrote:
> If it's a quantum computer, it may be able to execute
> all branches of the iteration in parallel. But it
> would only have a probability of returning the right
> answer (in other cases it would kill your cat).
I know somebody who would claim that _is_ the right answer.
--
Grant Edwards grant.b.edwards Yow! Hello, GORRY-O!!
at I'm a GENIUS from HARVARD!!
gmail.com
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| From | Rotwang <sg552@hotmail.co.uk> |
|---|---|
| Date | 2014-02-13 21:29 +0000 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <ldjdg5$n9e$1@dont-email.me> |
| In reply to | #66178 |
What's this? A discussion about angels dancing on a the head of a pin?
Great, I'm in.
On 13/02/2014 14:00, Marko Rauhamaa wrote:
> Oscar Benjamin <oscar.j.benjamin@gmail.com>:
>
>> This isn't even a question of resource constraints: a digital computer
>> with infinite memory and computing power would still be limited to
>> working with countable sets, and the real numbers are just not
>> countable. The fundamentally discrete nature of digital computers
>> prevents them from being able to truly handle real numbers and real
>> computation.
>
> Well, if your idealized, infinite, digital computer had ℵ₁ bytes of RAM
> and ran at ℵ₁ hertz and Python supported transfinite iteration, you
> could easily do reals:
>
> def real_sqrt(y):
> for x in continuum(0, max(1, y)):
> # Note: x is not traversed in the < order but some other
> # well-ordering, which has been proved to exist.
> if x * x == y:
> return x
> assert False
>
> The function could well return in finite time with a precise result for
> any given nonnegative real argument.
Minor point: ℵ₁ does not mean the cardinality c of the continuum, it
means the smallest cardinal larger than ℵ₀. It has been proved that the
question of whether ℵ₁ == c is independent of ZFC, so it is in a sense
unanswerable.
More importantly, though, such a computer could not complete the above
iteration in finite time unless time itself is not real-valued. That's
because if k is an uncountable ordinal then there is no strictly
order-preserving function from k to the unit interval [0, 1]. For
suppose otherwise, and let f be such a function. Let S denote the set of
successor ordinals in k, and let L denote the set of limit ordinals in
k. Then lambda x: x + 1 is an injective function from L (or L with a
single point removed if k is the successor of a limit ordinal) to S, so
that S is at least as large as L and since k == S | L it follows that S
is uncountable.
For each x + 1 in S, let g(x + 1) = f(x + 1) - f(x) > 0. Let F be any
finite subset of S and let y = max(F). It is clear that f(y) >= sum(g(x)
for x in F). Since also f(y) <= 1, we have sum(g(x) for x in F) if <= 1
for all finite F. In particular, for any integer n > 0, the set S_n = {x
for x in S if g(x) > 1/n} has len(S_n) < n. But then S is the union of
the countable collection {S_n for n in N} of finite sets, so is
countable; a contradiction.
On 13/02/2014 19:47, Marko Rauhamaa wrote:
> My assumption was you could execute ℵ₁ statements per second. That
> doesn't guarantee a finite finish time but would make it possible. That
> is because
>
> ℵ₁ * ℵ₁ = ℵ₁ = ℵ₁ * 1
I don't think that's enough - assuming the operations of your processor
during a second can be indexed by some ordinal k with len(k) == c, if
each of the c operations per iteration must be complete before the next
step of the for loop is complete then you need an injective function
from c * c to k that preserves the lexicographic ordering. I don't know
whether such a function exists for arbitrary such k, but k can be chosen
in advance so that it does.
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| From | Marko Rauhamaa <marko@pacujo.net> |
|---|---|
| Date | 2014-02-14 00:00 +0200 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <877g8y7jwa.fsf@elektro.pacujo.net> |
| In reply to | #66252 |
Rotwang <sg552@hotmail.co.uk>: >> for x in continuum(0, max(1, y)): >> # Note: x is not traversed in the < order but some other >> # well-ordering, which has been proved to exist. >> if x * x == y: >> return x > > [...] > > More importantly, though, such a computer could not complete the above > iteration in finite time unless time itself is not real-valued. That's > because if k is an uncountable ordinal then there is no strictly > order-preserving function from k to the unit interval [0, 1]. If you read the code comment above, the transfinite iterator yields the whole continuum, not in the < order (which is impossible), but in some other well-ordering (which is known to exist). Thus, we can exhaust the continuum in ℵ₁ discrete steps. (Yes, the continuum hypothesis was used to make the notation easier to read.) Marko
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| From | Rotwang <sg552@hotmail.co.uk> |
|---|---|
| Date | 2014-02-13 22:21 +0000 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <ldjghn$9f1$1@dont-email.me> |
| In reply to | #66261 |
On 13/02/2014 22:00, Marko Rauhamaa wrote: > Rotwang <sg552@hotmail.co.uk>: > >>> for x in continuum(0, max(1, y)): >>> # Note: x is not traversed in the < order but some other >>> # well-ordering, which has been proved to exist. >>> if x * x == y: >>> return x >> >> [...] Restoring for context: >>> The function could well return in finite time with a precise result >>> for any given nonnegative real argument. >> More importantly, though, such a computer could not complete the above >> iteration in finite time unless time itself is not real-valued. That's >> because if k is an uncountable ordinal then there is no strictly >> order-preserving function from k to the unit interval [0, 1]. > > If you read the code comment above, the transfinite iterator yields the > whole continuum, not in the < order (which is impossible), but in some > other well-ordering (which is known to exist). Thus, we can exhaust the > continuum in ℵ₁ discrete steps. Yes, I understood that. But my point was that it can't carry out those ℵ₁ discrete steps in finite time (assuming that time is real-valued), because there's no way to embed them in any time interval without changing their order. Note that this is different to the case of iterating over a countable set, since the unit interval does have countable well-ordered subsets.
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| From | Marko Rauhamaa <marko@pacujo.net> |
|---|---|
| Date | 2014-02-14 01:16 +0200 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <8738jm7gec.fsf@elektro.pacujo.net> |
| In reply to | #66263 |
Rotwang <sg552@hotmail.co.uk>: > But my point was that it can't carry out those ℵ₁ discrete steps in > finite time (assuming that time is real-valued), because there's no > way to embed them in any time interval without changing their order. I'd have to think so I take your word for it. Marko
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| From | Ben Finney <ben+python@benfinney.id.au> |
|---|---|
| Date | 2014-02-14 03:57 +1100 |
| Subject | Re: Working with the set of real numbers |
| Message-ID | <mailman.6848.1392310653.18130.python-list@python.org> |
| In reply to | #66004 |
Oscar Benjamin <oscar.j.benjamin@gmail.com> writes: > I think Chris' statement above is pretty clear. I disagree, as explained. > Also I didn't find the original statement confusing I'm happy for you. > and it is a reasonable point to make. Yes, and I was not addressing that. -- \ “It is well to remember that the entire universe, with one | `\ trifling exception, is composed of others.” —John Andrew Holmes | _o__) | Ben Finney
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| From | Ned Batchelder <ned@nedbatchelder.com> |
|---|---|
| Date | 2014-02-10 10:02 -0500 |
| Message-ID | <mailman.6625.1392044581.18130.python-list@python.org> |
| In reply to | #65815 |
On 2/10/14 9:43 AM, Tim Chase wrote:
> On 2014-02-10 06:07, wxjmfauth@gmail.com wrote:
>> Python does not save memory at all. A str (unicode string)
>> uses less memory only - and only - because and when one uses
>> explicitly characters which are consuming less memory.
>>
>> Not only the memory gain is zero, Python falls back to the
>> worse case.
>>
>>>>> sys.getsizeof('a' * 1000000)
>> 1000025
>>>>> sys.getsizeof('a' * 1000000 + 'oe')
>> 2000040
>>>>> sys.getsizeof('a' * 1000000 + 'oe' + '\U00010000')
>> 4000048
>
> If Python used UTF-32 for EVERYTHING, then all three of those cases
> would be 4000048, so it clearly disproves your claim that "python
> does not save memory at all".
>
>> The opposite of what the utf8/utf16 do!
>>
>>>>> sys.getsizeof(('a' * 1000000 + 'oe' +
>>>>> '\U00010000').encode('utf-8'))
>> 1000023
>>>>> sys.getsizeof(('a' * 1000000 + 'oe' +
>>>>> '\U00010000').encode('utf-16'))
>> 2000025
>
> However, as pointed out repeatedly, string-indexing in fixed-width
> encodings are O(1) while indexing into variable-width encodings (e.g.
> UTF8/UTF16) are O(N). The FSR gives the benefits of O(1) indexing
> while saving space when a string doesn't need to use a full 32-bit
> width.
>
> -tkc
>
>
>
Please don't engage in this debate with JMF. His mind is made up, and
he will not be swayed, no matter how persuasive and reasonable your
arguments. Just ignore him.
--
Ned Batchelder, http://nedbatchelder.com
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| From | Neil Cerutti <neilc@norwich.edu> |
|---|---|
| Date | 2014-02-11 14:29 +0000 |
| Message-ID | <mailman.6670.1392128988.18130.python-list@python.org> |
| In reply to | #65815 |
On 2014-02-10, Ned Batchelder <ned@nedbatchelder.com> wrote:
> On 2/10/14 9:43 AM, Tim Chase wrote:
>>> The opposite of what the utf8/utf16 do!
>>>
>>>>>> sys.getsizeof(('a' * 1000000 + 'oe' +
>>>>>> '\U00010000').encode('utf-8'))
>>> 1000023
>>>>>> sys.getsizeof(('a' * 1000000 + 'oe' +
>>>>>> '\U00010000').encode('utf-16'))
>>> 2000025
>>
>> However, as pointed out repeatedly, string-indexing in
>> fixed-width encodings are O(1) while indexing into
>> variable-width encodings (e.g. UTF8/UTF16) are O(N). The FSR
>> gives the benefits of O(1) indexing while saving space when a
>> string doesn't need to use a full 32-bit width.
>
> Please don't engage in this debate with JMF. His mind is made
> up, and he will not be swayed, no matter how persuasive and
> reasonable your arguments. Just ignore him.
I think reasonable criticisms should be contested no matter who
posts them. I agree jmf shouldn't be singled out for abuse,
summoned, insulted, or have his few controversial opinions
brought into other topics. Tim's post was responding to a
specific, well-presented criticism of Python's string
implementation. Left unchallenged, it might linger unhappily in
the air, like a symphony ended on a dominant 7th chord.
--
Neil Cerutti
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| From | Dennis Lee Bieber <wlfraed@ix.netcom.com> |
|---|---|
| Date | 2014-02-05 22:14 -0500 |
| Message-ID | <mailman.6433.1391656482.18130.python-list@python.org> |
| In reply to | #65474 |
On Wed, 5 Feb 2014 22:44:47 +1100, Chris Angelico <rosuav@gmail.com>
declaimed the following:
>On Wed, Feb 5, 2014 at 10:00 PM, Steven D'Aprano
><steve+comp.lang.python@pearwood.info> wrote:
>>> where stopWords.txt is a file of size 4KB
>>
>> My guess is that if you split a 4K file into words, then put the words
>> into a list, you'll probably end up with 6-8K in memory.
>
>I'd guess rather more; Python strings have a fair bit of fixed
>overhead, so with a whole lot of small strings, it will get more
>costly.
>
>>>> sys.version
>'3.4.0b2 (v3.4.0b2:ba32913eb13e, Jan 5 2014, 16:23:43) [MSC v.1600 32
>bit (Intel)]'
>>>> sys.getsizeof("asdf")
>29
>
>>> import sys
>>> indata = "221B or not to be seeing you again"
>>> sys.getsizeof(indata)
67
>>> worddata = indata.split()
>>> worddata
['221B', 'or', 'not', 'to', 'be', 'seeing', 'you', 'again']
>>> sys.getsizeof(worddata) + sum(sys.getsizeof(wd) for wd in worddata)
451
That's a 7X expansion for just splitting a single line into a list of
words.
--
Wulfraed Dennis Lee Bieber AF6VN
wlfraed@ix.netcom.com HTTP://wlfraed.home.netcom.com/
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| From | Dave Angel <davea@davea.name> |
|---|---|
| Date | 2014-02-05 08:43 -0500 |
| Message-ID | <mailman.6420.1391607624.18130.python-list@python.org> |
| In reply to | #65470 |
Ayushi Dalmia <ayushidalmia2604@gmail.com> Wrote in message:
> On Wednesday, February 5, 2014 12:59:46 AM UTC+5:30, Tim Chase wrote:
>> On 2014-02-04 14:21, Dave Angel wrote:
>>
>> > To get the "total" size of a list of strings, try (untested):
>>
>> >
>>
>> > a = sys.getsizeof (mylist )
>>
>> > for item in mylist:
>>
>> > a += sys.getsizeof (item)
>>
>>
>>
>> I always find this sort of accumulation weird (well, at least in
>>
>> Python; it's the *only* way in many other languages) and would write
>>
>> it as
>>
>>
>>
>> a = getsizeof(mylist) + sum(getsizeof(item) for item in mylist)
>>
>>
>>
>> -tkc
>
> This also doesn't gives the true size. I did the following:
>
> import sys
> data=[]
> f=open('stopWords.txt','r')
>
> for line in f:
> line=line.split()
> data.extend(line)
>
> print sys.getsizeof(data)
>
Did you actually READ either of my posts or Tim's? For a
container, you can't just use getsizeof on the container.
a = sys.getsizeof (data)
for item in mylist:
a += sys.getsizeof (data)
print a
--
DaveA
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| From | Ayushi Dalmia <ayushidalmia2604@gmail.com> |
|---|---|
| Date | 2014-02-05 06:33 -0800 |
| Message-ID | <e83e857f-f0e0-4aa7-8955-dcb9922a655c@googlegroups.com> |
| In reply to | #65477 |
On Wednesday, February 5, 2014 7:13:34 PM UTC+5:30, Dave Angel wrote:
> Ayushi Dalmia <ayushidalmia2604@gmail.com> Wrote in message:
>
> > On Wednesday, February 5, 2014 12:59:46 AM UTC+5:30, Tim Chase wrote:
>
> >> On 2014-02-04 14:21, Dave Angel wrote:
>
> >>
>
> >> > To get the "total" size of a list of strings, try (untested):
>
> >>
>
> >> >
>
> >>
>
> >> > a = sys.getsizeof (mylist )
>
> >>
>
> >> > for item in mylist:
>
> >>
>
> >> > a += sys.getsizeof (item)
>
> >>
>
> >>
>
> >>
>
> >> I always find this sort of accumulation weird (well, at least in
>
> >>
>
> >> Python; it's the *only* way in many other languages) and would write
>
> >>
>
> >> it as
>
> >>
>
> >>
>
> >>
>
> >> a = getsizeof(mylist) + sum(getsizeof(item) for item in mylist)
>
> >>
>
> >>
>
> >>
>
> >> -tkc
>
> >
>
> > This also doesn't gives the true size. I did the following:
>
> >
>
> > import sys
>
> > data=[]
>
> > f=open('stopWords.txt','r')
>
> >
>
> > for line in f:
>
> > line=line.split()
>
> > data.extend(line)
>
> >
>
> > print sys.getsizeof(data)
>
> >
>
>
>
> Did you actually READ either of my posts or Tim's? For a
>
> container, you can't just use getsizeof on the container.
>
>
>
>
>
> a = sys.getsizeof (data)
>
> for item in mylist:
>
> a += sys.getsizeof (data)
>
> print a
>
>
>
> --
>
> DaveA
Yes, I did. I now understand how to find the size.
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| From | Mark Lawrence <breamoreboy@yahoo.co.uk> |
|---|---|
| Date | 2014-02-05 15:22 +0000 |
| Message-ID | <mailman.6421.1391613798.18130.python-list@python.org> |
| In reply to | #65478 |
On 05/02/2014 14:33, Ayushi Dalmia wrote: Please stop sending double line spaced messages, just follow the instructions here https://wiki.python.org/moin/GoogleGroupsPython to prevent this happening, thanks. -- My fellow Pythonistas, ask not what our language can do for you, ask what you can do for our language. Mark Lawrence
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