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Finding size of Variable

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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

Page 7 of 7 — ← Prev page 1 2 3 4 5 6 [7]

#67783 — Re: Working with the set of real numbers

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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#66285 — Re: Working with the set of real numbers

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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#66286 — Re: Working with the set of real numbers

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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#66298 — Re: Working with the set of real numbers

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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#66294 — Re: Working with the set of real numbers

 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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#66297 — Re: Working with the set of real numbers

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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#66252 — Re: Working with the set of real numbers

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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#66261 — Re: Working with the set of real numbers

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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#66263 — Re: Working with the set of real numbers

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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#66269 — Re: Working with the set of real numbers

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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#66191 — Re: Working with the set of real numbers

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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#65821

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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#65910

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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#65504

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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#65477

 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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#65478

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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#65480

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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