On Thu, Mar 6, 2014 at 11:27 PM, Oscar Benjamin
wrote:
> So my loop
>
> while x ** 2 - y > x * eps:
> x = (x + y/x) / 2
>
> and Chris' loop:
>
> while abs(guess1-guess2) > epsilon:
> guess1 = n/guess2
> guess2 = (guess1 + guess2)/2
>
> and now your loop
>
>
On 5 March 2014 12:57, Dave Angel wrote:
> Oscar Benjamin Wrote in message:
>> On 4 March 2014 23:20, Dave Angel wrote:
>>>
>>> On the assumption that division by 2 is very fast, and that a
>>> general multiply isn't too bad, you could improve on Newton by
>>> observing that the slope is 2.
In article <5317e640$0$29985$c3e8da3$54964...@news.astraweb.com>,
Steven D'Aprano wrote:
> On Wed, 05 Mar 2014 21:31:51 -0500, Roy Smith wrote:
>
> > In article <53176225$0$29987$c3e8da3$54964...@news.astraweb.com>,
> > Steven D'Aprano wrote:
> >
> >> Physics is the fundamental science, at l
On 2014-03-06, Roy Smith wrote:
> In article <53176225$0$29987$c3e8da3$54964...@news.astraweb.com>,
> Steven D'Aprano wrote:
>
>> Physics is the fundamental science, at least according to the
>> physicists, and Real Soon Now they'll have a Theory Of Everything,
>> something small enough to print
On Thu, Mar 6, 2014 at 2:06 PM, Steven D'Aprano
wrote:
> They ask a computer programmer to adjudicate who is right, so he writes a
> program to print out all the primes:
>
> 1 is prime
> 1 is prime
> 1 is prime
> 1 is prime
> 1 is prime
And he claimed that he was correct, because he had - as is k
On Wed, 05 Mar 2014 21:31:51 -0500, Roy Smith wrote:
> In article <53176225$0$29987$c3e8da3$54964...@news.astraweb.com>,
> Steven D'Aprano wrote:
>
>> Physics is the fundamental science, at least according to the
>> physicists, and Real Soon Now they'll have a Theory Of Everything,
>> something
In article <53176225$0$29987$c3e8da3$54964...@news.astraweb.com>,
Steven D'Aprano wrote:
> Physics is the fundamental science, at least according to the physicists,
> and Real Soon Now they'll have a Theory Of Everything, something small
> enough to print on a tee-shirt, which will explain eve
On 5 March 2014 17:43, Steven D'Aprano
wrote:
> On Wed, 05 Mar 2014 12:21:37 +, Oscar Benjamin wrote:
>>
>> The argument that the sum of all natural numbers comes to -1/12 is just
>> some kind of hoax. I don't think *anyone* seriously believes it.
>
> You would be wrong. I suggest you read the
On 2014-03-05, Chris Kaynor wrote:
> On Wed, Mar 5, 2014 at 9:43 AM, Steven D'Aprano <
> steve+comp.lang.pyt...@pearwood.info> wrote:
>
>> At one time, Euler summed an infinite series and got -1, from which he
>> concluded that -1 was (in some sense) larger than infinity. I don't know
>> what just
On Wed, Mar 5, 2014 at 9:43 AM, Steven D'Aprano <
steve+comp.lang.pyt...@pearwood.info> wrote:
> At one time, Euler summed an infinite series and got -1, from which he
> concluded that -1 was (in some sense) larger than infinity. I don't know
> what justification he gave, but the way I think of it
On Thu, Mar 6, 2014 at 4:43 AM, Steven D'Aprano
wrote:
> Physics is the fundamental science, at least according to the physicists,
> and Real Soon Now they'll have a Theory Of Everything, something small
> enough to print on a tee-shirt, which will explain everything. At least
> in principle.
Eve
On Wed, 05 Mar 2014 12:50:06 +, Mark Lawrence wrote:
> On 05/03/2014 12:21, Oscar Benjamin wrote:
>>
>> Why the dig at physicists? I think most physicists would be able to
>> tell you that the sum of all natural numbers is not -1/12. In fact most
>> people with very little background in mathem
On Wed, 05 Mar 2014 12:21:37 +, Oscar Benjamin wrote:
> On 5 March 2014 07:52, Steven D'Aprano wrote:
>> On Tue, 04 Mar 2014 23:25:37 -0500, Roy Smith wrote:
>>
>>> I stopped paying attention to mathematicians when they tried to
>>> convince me that the sum of all natural numbers is -1/12.
>>
Dave Angel Wrote in message:
> Oscar Benjamin Wrote in message:
>> On 4 March 2014 23:20, Dave Angel wrote:
>>>
>>> If anyone is curious, I'll be glad to describe the algorithm;
>>> I've never seen it published, before or since. I got my
>>> inspiration from a method used in mechanical,
Oscar Benjamin Wrote in message:
> On 4 March 2014 23:20, Dave Angel wrote:
>>
>> One problem with complexity claims is that it's easy to miss some
>> contributing time eaters. I haven't done any measuring on modern
>> machines nor in python, but I'd assume that multiplies take
>> *much* long
On 05/03/2014 12:21, Oscar Benjamin wrote:
Why the dig at physicists? I think most physicists would be able to
tell you that the sum of all natural numbers is not -1/12. In fact
most people with very little background in mathematics can tell you
that.
I'll put that one to the test tomorrow mo
On 5 March 2014 07:52, Steven D'Aprano wrote:
> On Tue, 04 Mar 2014 23:25:37 -0500, Roy Smith wrote:
>
>> I stopped paying attention to mathematicians when they tried to convince
>> me that the sum of all natural numbers is -1/12.
>
> I'm pretty sure they did not. Possibly a physicist may have tri
On 4 March 2014 23:20, Dave Angel wrote:
>
> One problem with complexity claims is that it's easy to miss some
> contributing time eaters. I haven't done any measuring on modern
> machines nor in python, but I'd assume that multiplies take
> *much* longer for large integers, and that divides ar
On 3/5/14 4:00 AM, wxjmfa...@gmail.com wrote:
Mathematics?
The Flexible String Representation is a very nice example
of a mathematical absurdity.
jmf
PS Do not even think to expect to contradict me. Hint:
sheet of paper and pencil.
Reminder to everyone: JMF makes no sense when he talks about
Mathematics?
The Flexible String Representation is a very nice example
of a mathematical absurdity.
jmf
PS Do not even think to expect to contradict me. Hint:
sheet of paper and pencil.
--
https://mail.python.org/mailman/listinfo/python-list
Following up on my own post.
On Wed, 05 Mar 2014 07:52:01 +, Steven D'Aprano wrote:
> On Tue, 04 Mar 2014 23:25:37 -0500, Roy Smith wrote:
>
>> I stopped paying attention to mathematicians when they tried to
>> convince me that the sum of all natural numbers is -1/12.
[...]
> In effect, the
On Tue, 04 Mar 2014 23:25:37 -0500, Roy Smith wrote:
> I stopped paying attention to mathematicians when they tried to convince
> me that the sum of all natural numbers is -1/12.
I'm pretty sure they did not. Possibly a physicist may have tried to tell
you that, but most mathematicians conside
In article ,
Ben Finney wrote:
> Roy Smith writes:
>
> > I stopped paying attention to mathematicians when they tried to convince
> > me that the sum of all natural numbers is -1/12.
>
> I stopped paying attention to a particular person when they said âI
> stopped paying attention to an en
On Wednesday, March 5, 2014 10:07:44 AM UTC+5:30, Ben Finney wrote:
> Roy Smith writes:
> > I stopped paying attention to mathematicians when they tried to convince
> > me that the sum of all natural numbers is -1/12.
> I stopped paying attention to a particular person when they said "I
> stoppe
Roy Smith writes:
> I stopped paying attention to mathematicians when they tried to convince
> me that the sum of all natural numbers is -1/12.
I stopped paying attention to a particular person when they said “I
stopped paying attention to an entire field of study because one
position expressed
In article ,
Rustom Mody wrote:
> I cannot find the exact quote so from memory Weyl says something to this
> effect:
>
> Cantor's diagonalization PROOF is not in question.
> Its CONCLUSION very much is.
> The classical/platonic mathematician (subject to wooly thinking) concludes
> that
> the
On Wednesday, March 5, 2014 9:11:13 AM UTC+5:30, Steven D'Aprano wrote:
> On Wed, 05 Mar 2014 02:15:14 +, Albert van der Horst wrote:
> > Adding cf's adds all computable numbers in infinite precision. However
> > that is not even a drop in the ocean, as the computable numbers have
> > measure
On Wed, 05 Mar 2014 02:15:14 +, Albert van der Horst wrote:
> Adding cf's adds all computable numbers in infinite precision. However
> that is not even a drop in the ocean, as the computable numbers have
> measure zero.
On the other hand, it's not really clear that the non-computable numbers
In article <87fvnm7q1n@elektro.pacujo.net>,
Marko Rauhamaa wrote:
>Chris Angelico :
>
>> On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa wrote:
>>> Well, if your idealized, infinite, digital computer had âµâ bytes of RAM
>>> and ran at âµâ hertz and Python supported transfinite iterati
In article ,
Chris Angelico wrote:
>On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst
> wrote:
>>>No, the Python built-in float type works with a subset of real numbers:
>>
>> To be more precise: a subset of the rational numbers, those with a
>> denominator
>> that is a power of two.
>
>And n
In article ,
Ian Kelly wrote:
>On Mon, Mar 3, 2014 at 11:35 PM, Chris Angelico wrote:
>> In constant space, that will produce the sum of two infinite sequences
>> of digits. (And it's constant time, too, except when it gets a stream
>> of nines. Adding three thirds together will produce an infin
Oscar Benjamin Wrote in message:
> On 4 March 2014 21:18, Chris Angelico wrote:
>
>
> It does not take O(n*n) time. This is Newton iteration and for
> well-behaved problems such as this it generates more than n digits
> after n iterations. I modified my code to show the error (x**2 - y) at
> ea
On Wed, Mar 5, 2014 at 9:54 AM, Oscar Benjamin
wrote:
>> Let's compare two
>> versions. In the first, you set the precision (I'm talking in terms of
>> REXX's "NUMERIC DIGITS" statement
>
> I have no idea what that is.
>
>>- anything beyond this many digits
>> will be rounded (and represented expo
On 4 March 2014 22:18, Chris Angelico wrote:
> On Wed, Mar 5, 2014 at 9:02 AM, Oscar Benjamin
> wrote:
>> On 4 March 2014 21:18, Chris Angelico wrote:
>>> On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
>>> wrote:
>>>
>>> epsilon = 0.0001
>>> def sqrt(n):
>>> guess1, guess2 = 1, n
>>> wh
On Wed, Mar 5, 2014 at 9:02 AM, Oscar Benjamin
wrote:
> On 4 March 2014 21:18, Chris Angelico wrote:
>> On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
>> wrote:
>>> I don't quite follow your reasoning here. By "cut-and-try" do you mean
>>> bisection? If so it gives the first N decimal digits in
On 4 March 2014 21:05, Marko Rauhamaa wrote:
> Oscar Benjamin :
>
>> To me the obvious method is Newton iteration which takes O(sqrt(N))
>> iterations to obtain N digits of precision. This brings the above
>> complexity below quadratic:
>>
>> #!/usr/bin/env python
>>
>> from decimal import Decimal
On 4 March 2014 21:18, Chris Angelico wrote:
> On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
> wrote:
>> I don't quite follow your reasoning here. By "cut-and-try" do you mean
>> bisection? If so it gives the first N decimal digits in N*log2(10)
>> iterations. However each iteration requires a m
On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
wrote:
> I don't quite follow your reasoning here. By "cut-and-try" do you mean
> bisection? If so it gives the first N decimal digits in N*log2(10)
> iterations. However each iteration requires a multiply and when the
> number of digits N becomes lar
Oscar Benjamin :
> To me the obvious method is Newton iteration which takes O(sqrt(N))
> iterations to obtain N digits of precision. This brings the above
> complexity below quadratic:
>
> #!/usr/bin/env python
>
> from decimal import Decimal as D, localcontext
>
> def sqrt(y, prec=1000):
> ''
On 4 March 2014 19:58, Chris Angelico wrote:
> On Wed, Mar 5, 2014 at 6:49 AM, Marko Rauhamaa wrote:
>> Chris Angelico :
>>
>>> As far as I know, there's no simple way, in constant space and/or
>>> time, to progressively yield more digits of a number's square root,
>>> working in decimal.
>>
>> I
On Wed, Mar 5, 2014 at 6:49 AM, Marko Rauhamaa wrote:
> Chris Angelico :
>
>> As far as I know, there's no simple way, in constant space and/or
>> time, to progressively yield more digits of a number's square root,
>> working in decimal.
>
> I don't know why the constant space/time requirement is
Chris Angelico :
> As far as I know, there's no simple way, in constant space and/or
> time, to progressively yield more digits of a number's square root,
> working in decimal.
I don't know why the constant space/time requirement is crucial. Anyway,
producing more digits simple: http://nrich.math
On Tue, Mar 4, 2014 at 10:05 PM, Gregory Ewing
wrote:
> Chris Angelico wrote:
>>
>> In constant space, that will produce the sum of two infinite sequences
>> of digits.
>
>
> It's not constant space, because the nines counter
> can grow infinitely large.
Okay, okay, technically yes. But the count
On Tue, Mar 4, 2014 at 4:19 AM, Ian Kelly wrote:
> def cf_sqrt(n):
> """Yield the terms of the square root of n as a continued fraction."""
>m = 0
> d = 1
> a = a0 = floor_sqrt(n)
> while True:
> yield a
> next_m = d * a - m
> next_d = (n - next_m * next
On Mon, Mar 3, 2014 at 11:35 PM, Chris Angelico wrote:
> In constant space, that will produce the sum of two infinite sequences
> of digits. (And it's constant time, too, except when it gets a stream
> of nines. Adding three thirds together will produce an infinite loop
> as it waits to see if the
Chris Angelico wrote:
In constant space, that will produce the sum of two infinite sequences
of digits.
It's not constant space, because the nines counter
can grow infinitely large.
--
Greg
--
https://mail.python.org/mailman/listinfo/python-list
On Tue, Mar 4, 2014 at 4:53 PM, Steven D'Aprano wrote:
> On Tue, 04 Mar 2014 14:46:25 +1100, Chris Angelico wrote:
>
>> That's neat, didn't know that. Is there an efficient way to figure out,
>> for any integer N, what its sqrt's CF sequence is? And what about the
>> square roots of non-integers -
On Tue, 04 Mar 2014 14:46:25 +1100, Chris Angelico wrote:
> That's neat, didn't know that. Is there an efficient way to figure out,
> for any integer N, what its sqrt's CF sequence is? And what about the
> square roots of non-integers - can you represent √π that way? I suspect,
> though I can't pr
On Tuesday, March 4, 2014 9:16:25 AM UTC+5:30, Chris Angelico wrote:
> On Tue, Mar 4, 2014 at 2:13 PM, Rustom Mody wrote:
> >> But it's a far cry from "all real numbers". Even allowing for
> >> continued fractions adds only some more; I don't think you can
> >> represent surds that way.
> > See
>
On Tue, Mar 4, 2014 at 2:13 PM, Rustom Mody wrote:
>> But it's a far cry from "all real numbers". Even allowing for
>> continued fractions adds only some more; I don't think you can
>> represent surds that way.
>
> See
>
> http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html#s
On Tuesday, March 4, 2014 8:32:01 AM UTC+5:30, Chris Angelico wrote:
> On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst wrote:
> >>No, the Python built-in float type works with a subset of real numbers:
> > To be more precise: a subset of the rational numbers, those with a
> > denominator
> >
On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst
wrote:
>>No, the Python built-in float type works with a subset of real numbers:
>
> To be more precise: a subset of the rational numbers, those with a denominator
> that is a power of two.
And no more than N bits (53 in a 64-bit float) in the
In article ,
Chris Angelico wrote:
>On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney wrote:
>> Chris Angelico writes:
>>
>>> I have yet to find any computer that works with the set of real
>>> numbers in any way. Never mind optimization, they simply cannot work
>>> with real numbers.
>>
>> Not *any*
On Fri, Feb 14, 2014 at 3:30 AM, Gregory Ewing
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
>> i
On 2014-02-14, Gregory Ewing 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 r
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!
--
https://mail.python.org/mailman/listinfo/python-list
Chris Angelico 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 yo
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
On Fri, Feb 14, 2014 at 5:37 PM, Gregory Ewing
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
>>
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
On Thu, Feb 13, 2014 at 11:47 AM, Marko Rauhamaa wrote:
> Chris Angelico :
>
>> On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa 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 easi
Dave Angel wrote:
Actually, the particular example you use can be done. When
printing the infinite sum of two infinite decimal streams, you
can simply hold back whenever you get one or more nines.
But you only have a finite amount of space for keeping
track of how many nines you've seen, so
Rotwang :
> 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
--
https://mail.pytho
On 13/02/2014 22:00, Marko Rauhamaa wrote:
Rotwang :
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
[...]
Rotwang :
>> 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
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 :
This isn't even a question of resource constraints: a digital computer
with infinite memory and computing power would still be limited to
working w
On Fri, Feb 14, 2014 at 6:47 AM, 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
Hmm. I never actually covered this stuff in grade school
Chris Angelico :
> On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa 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)):
>
>
On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa 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:
>
> def real_sqrt(y):
> for x in continuum(0, max(1, y)):
>
Oscar Benjamin 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 tha
Oscar Benjamin :
> 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
> prev
On 12 February 2014 10:07, Ben Finney wrote:
> Chris Angelico writes:
>
>> On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney
>> wrote:
>> > So, if I understand you right, you want to say that you've not found
>> > a computer that works with the *complete* set of real numbers. Yes?
>>
>> Correct. [...
On Thu, Feb 13, 2014 at 2:31 PM, Steven D'Aprano wrote:
> "The former South African apartheid government did not respect the
> Universal Human Rights of blacks."
>
> Under your strict interpretation, we would have to say that even a single
> example of the apartheid government respecting even a si
Steven D'Aprano writes:
> On Wed, 12 Feb 2014 21:07:04 +1100, Ben Finney wrote:
>
> > You've done it again: by saying that “computers *do not* work with
> > real numbers”, that if I find a real number – e.g. the number 4 –
> > your position is that, since it's a real number, computers don't
> > w
On Wed, 12 Feb 2014 21:07:04 +1100, Ben Finney wrote:
> Chris Angelico writes:
>
>> On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney
>> wrote:
>> > So, if I understand you right, you want to say that you've not found
>> > a computer that works with the *complete* set of real numbers. Yes?
>>
>> Corr
On Thursday, February 13, 2014 2:15:28 AM UTC+5:30, Ian wrote:
> On Wed, Feb 12, 2014 at 7:11 AM, Rustom Mody wrote:
> > On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote:
> >> Chris Angelico writes:
> >> > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote:
> >> > > So, if I u
On 2014-02-12, Gregory Ewing wrote:
> Chris Angelico wrote:
>
>> Of course a computer can work with _some_ real numbers; but only
>> some. (An awful lot of them, of course. A ridiculously huge number of
>> numbers. More numbers than you could read in a lifetime! While the
>> number is extremely la
Gregory Ewing Wrote in message:
> Chris Angelico wrote:
>> Sure, but nobody said the text file had to be _stored_ anywhere :)
>> Computers are quite capable of working with streams of incoming data
>> that are potentially infinite in size.
>
> However, they *can't* work with arbitrary real numbe
Chris Angelico wrote:
Of course a
computer can work with _some_ real numbers; but only some. (An awful
lot of them, of course. A ridiculously huge number of numbers. More
numbers than you could read in a lifetime! While the number is
extremely large, it still falls pitifully short of infinity.[1]
Chris Angelico wrote:
Sure, but nobody said the text file had to be _stored_ anywhere :)
Computers are quite capable of working with streams of incoming data
that are potentially infinite in size.
However, they *can't* work with arbitrary real numbers in an
exact way, even if they are represent
Ben Finney wrote:
That's why I think you need to be clear that your point isn't “computers
don't work with real numbers”, but rather “computers work only with a
limited subset of real numbers”.
They actually work with a subset of *rational* numbers.
All floats representable by a computer are ra
On Wed, Feb 12, 2014 at 7:11 AM, Rustom Mody wrote:
> On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote:
>> Chris Angelico writes:
>
>> > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote:
>> > > So, if I understand you right, you want to say that you've not found
>> > > a com
On Thu, Feb 13, 2014 at 1:13 AM, Marko Rauhamaa wrote:
> Text files suffer from the same caveat as integers: there's a limit to
> how much you can store on the physical computer.
Sure, but nobody said the text file had to be _stored_ anywhere :)
Computers are quite capable of working with streams
"Grant Edwards" wrote:
Not *any* computer? Not in *any* way? The Python built-in "float"
type "works with the set of real numbers", in a way.
The only people who think that are people who don't actualy _use_
floating point types on computers.
FPU parsing the IEEE spec, or?. I didn't quite pa
On 2014-02-12, Ben Finney wrote:
> Chris Angelico writes:
>
>> I have yet to find any computer that works with the set of real
>> numbers in any way. Never mind optimization, they simply cannot work
>> with real numbers.
>
> Not *any* computer? Not in *any* way? The Python built-in "float"
> type
Chris Angelico :
> On Wed, Feb 12, 2014 at 11:48 PM, Marko Rauhamaa wrote:
>> According to your definition, there's no computer in the world that can
>> work with integers or text files.
>
> Integers as far as RAM will allow, usually (which is the same caveat
> as is used when describing a progra
On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote:
> Chris Angelico writes:
> > On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote:
> > > So, if I understand you right, you want to say that you've not found
> > > a computer that works with the *complete* set of real numbers. Ye
On Wed, Feb 12, 2014 at 11:48 PM, Marko Rauhamaa wrote:
> Chris Angelico :
>
>> 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
>> t
Chris Angelico :
> 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
On Wed, Feb 12, 2014 at 10:44 PM, Ben Finney wrote:
> Chris Angelico writes:
>
>> On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney
>> wrote:
>> > That's why I think you need to be clear that your point isn't
>> > “computers don't work with real numbers”, but rather “computers work
>> > only with a l
On 2/12/14 5:55 AM, wxjmfa...@gmail.com wrote:
The fascinating aspect of this FSR lies
in its mathematical absurdity.
jmf
Stop.
--
Ned Batchelder, http://nedbatchelder.com
--
https://mail.python.org/mailman/listinfo/python-list
Chris Angelico writes:
> On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney
> wrote:
> > That's why I think you need to be clear that your point isn't
> > “computers don't work with real numbers”, but rather “computers work
> > only with a limited subset of real numbers”.
>
> Hmm, I'm not sure that my
The fascinating aspect of this FSR lies
in its mathematical absurdity.
jmf
--
https://mail.python.org/mailman/listinfo/python-list
On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney wrote:
> Chris Angelico writes:
>
>> On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney
>> wrote:
>> > So, if I understand you right, you want to say that you've not found
>> > a computer that works with the *complete* set of real numbers. Yes?
>>
>> Correct
Chris Angelico writes:
> On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney
> wrote:
> > So, if I understand you right, you want to say that you've not found
> > a computer that works with the *complete* set of real numbers. Yes?
>
> Correct. […] My point is that computers *do not* work with real
> nu
Chris Angelico writes:
> On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney wrote:
> > What specific behaviour would, for you, qualify as “works with the
> > set of real numbers in any way”?
>
> Being able to represent surds, pi, e, etc, for a start. It'd
> theoretically be possible with an algebraic not
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote:
> So, if I understand you right, you want to say that you've not found a
> computer that works with the *complete* set of real numbers. Yes?
Correct. When jmf referred to real numbers, he implied that there are
no optimizations done for natural n
Chris Angelico writes:
> On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney
> wrote:
> > Chris Angelico writes:
> >
> >> I have yet to find any computer that works with the set of real
> >> numbers in any way. Never mind optimization, they simply cannot
> >> work with real numbers.
> >
> > Not *any*
wxjmfa...@gmail.com writes:
> (2) is an artificial construct working
> with 3 sets (unicode).
jmf, you are being exceedingly disruptive: attempting to derail
unrelated discussions for your favourite hobby-horse topic. Please stop.
Everyone else: Please don't engage these attempts; instead, avoid
Le mercredi 12 février 2014 09:35:38 UTC+1, wxjm...@gmail.com a écrit :
> Integers are integers. (1)
>
> Characters are characters. (2)
>
>
>
> (1) is a unique "natural" set.
>
>
>
> (2) is an artificial construct working
>
> with 3 sets (unicode).
>
>
>
> jmf
Addendum: One should not c
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