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Re: Working with the set of real numbers

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Date Wed, 12 Feb 2014 21:20:19 +1100
Subject Re: Working with the set of real numbers
From Chris Angelico <rosuav@gmail.com>
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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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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 (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 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

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