On 5 March 2014 12:57, Dave Angel da...@davea.name wrote:
Oscar Benjamin oscar.j.benja...@gmail.com Wrote in message:
On 4 March 2014 23:20, Dave Angel da...@davea.name wrote:
On the assumption that division by 2 is very fast, and that a
general multiply isn't too bad, you could improve on
On Thu, Mar 6, 2014 at 11:27 PM, Oscar Benjamin
oscar.j.benja...@gmail.com 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
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 author
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
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
On 4 March 2014 23:20, Dave Angel da...@davea.name 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
On 5 March 2014 07:52, Steven D'Aprano st...@pearwood.info 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
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
Oscar Benjamin oscar.j.benja...@gmail.com Wrote in message:
On 4 March 2014 23:20, Dave Angel da...@davea.name 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
Dave Angel da...@davea.name Wrote in message:
Oscar Benjamin oscar.j.benja...@gmail.com Wrote in message:
On 4 March 2014 23:20, Dave Angel da...@davea.name 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
On Wed, 05 Mar 2014 12:21:37 +, Oscar Benjamin wrote:
On 5 March 2014 07:52, Steven D'Aprano st...@pearwood.info 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
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 mathematics
On Thu, Mar 6, 2014 at 4:43 AM, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info wrote:
Physics is the fundamental science, at least according to the physicists,
and Real Soon Now they'll have a Theory Of Everything, something small
enough to print on a tee-shirt, which will explain
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 is
On 2014-03-05, Chris Kaynor ckay...@zindagigames.com 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
On 5 March 2014 17:43, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info 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
In article 53176225$0$29987$c3e8da3$54964...@news.astraweb.com,
Steven D'Aprano steve+comp.lang.pyt...@pearwood.info wrote:
Physics is the fundamental science, at least according to the physicists,
and Real Soon Now they'll have a Theory Of Everything, something small
enough to print on a
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 steve+comp.lang.pyt...@pearwood.info wrote:
Physics is the fundamental science, at least according to the
physicists, and Real Soon Now they'll have a Theory
On Thu, Mar 6, 2014 at 2:06 PM, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info wrote:
They ask a computer programmer to adjudicate who is right, so he writes a
program to print out all the primes:
1 is prime
1 is prime
1 is prime
1 is prime
1 is prime
And he claimed that he was
On 2014-03-06, Roy Smith r...@panix.com wrote:
In article 53176225$0$29987$c3e8da3$54964...@news.astraweb.com,
Steven D'Aprano steve+comp.lang.pyt...@pearwood.info wrote:
Physics is the fundamental science, at least according to the
physicists, and Real Soon Now they'll have a Theory Of
In article 5317e640$0$29985$c3e8da3$54964...@news.astraweb.com,
Steven D'Aprano steve+comp.lang.pyt...@pearwood.info 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
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 Mon, Mar 3, 2014 at 11:35 PM, Chris Angelico ros...@gmail.com 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
On Tue, Mar 4, 2014 at 4:19 AM, Ian Kelly ian.g.ke...@gmail.com 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
On Tue, Mar 4, 2014 at 10:05 PM, Gregory Ewing
greg.ew...@canterbury.ac.nz 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
Chris Angelico ros...@gmail.com:
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:
On Wed, Mar 5, 2014 at 6:49 AM, Marko Rauhamaa ma...@pacujo.net wrote:
Chris Angelico ros...@gmail.com:
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
On 4 March 2014 19:58, Chris Angelico ros...@gmail.com wrote:
On Wed, Mar 5, 2014 at 6:49 AM, Marko Rauhamaa ma...@pacujo.net wrote:
Chris Angelico ros...@gmail.com:
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
Oscar Benjamin oscar.j.benja...@gmail.com:
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,
On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
oscar.j.benja...@gmail.com 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
On 4 March 2014 21:18, Chris Angelico ros...@gmail.com wrote:
On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
oscar.j.benja...@gmail.com 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.
On 4 March 2014 21:05, Marko Rauhamaa ma...@pacujo.net wrote:
Oscar Benjamin oscar.j.benja...@gmail.com:
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
On Wed, Mar 5, 2014 at 9:02 AM, Oscar Benjamin
oscar.j.benja...@gmail.com wrote:
On 4 March 2014 21:18, Chris Angelico ros...@gmail.com wrote:
On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
oscar.j.benja...@gmail.com wrote:
I don't quite follow your reasoning here. By cut-and-try do you mean
On 4 March 2014 22:18, Chris Angelico ros...@gmail.com wrote:
On Wed, Mar 5, 2014 at 9:02 AM, Oscar Benjamin
oscar.j.benja...@gmail.com wrote:
On 4 March 2014 21:18, Chris Angelico ros...@gmail.com wrote:
On Wed, Mar 5, 2014 at 7:55 AM, Oscar Benjamin
oscar.j.benja...@gmail.com wrote:
On Wed, Mar 5, 2014 at 9:54 AM, Oscar Benjamin
oscar.j.benja...@gmail.com 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
Oscar Benjamin oscar.j.benja...@gmail.com Wrote in message:
On 4 March 2014 21:18, Chris Angelico ros...@gmail.com 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
In article mailman.7702.1393932047.18130.python-l...@python.org,
Ian Kelly ian.g.ke...@gmail.com wrote:
On Mon, Mar 3, 2014 at 11:35 PM, Chris Angelico ros...@gmail.com wrote:
In constant space, that will produce the sum of two infinite sequences
of digits. (And it's constant time, too, except
In article mailman.7687.1393902132.18130.python-l...@python.org,
Chris Angelico ros...@gmail.com wrote:
On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst
alb...@spenarnc.xs4all.nl wrote:
No, the Python built-in float type works with a subset of real numbers:
To be more precise: a subset of
In article 87fvnm7q1n@elektro.pacujo.net,
Marko Rauhamaa ma...@pacujo.net wrote:
Chris Angelico ros...@gmail.com:
On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa ma...@pacujo.net wrote:
Well, if your idealized, infinite, digital computer had âµâ bytes of RAM
and ran at âµâ hertz and
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
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 zero.
In article c39d5b44-6c7b-40d1-bbb5-791a36af6...@googlegroups.com,
Rustom Mody rustompm...@gmail.com 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
Roy Smith r...@panix.com 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
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
stopped
In article mailman.7792.1393994283.18130.python-l...@python.org,
Ben Finney ben+pyt...@benfinney.id.au wrote:
Roy Smith r...@panix.com 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
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 consider
In article mailman.6735.1392194885.18130.python-l...@python.org,
Chris Angelico ros...@gmail.com wrote:
On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney ben+pyt...@benfinney.id.au wrote:
Chris Angelico ros...@gmail.com writes:
I have yet to find any computer that works with the set of real
numbers
On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst
alb...@spenarnc.xs4all.nl 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
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
that is a
On Tue, Mar 4, 2014 at 2:13 PM, Rustom Mody rustompm...@gmail.com 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 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, 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
On Tue, Mar 4, 2014 at 4:53 PM, Steven D'Aprano st...@pearwood.info 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
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
Chris Angelico ros...@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
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
On 2014-02-14, Gregory Ewing greg.ew...@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
On Fri, Feb 14, 2014 at 3:30 AM, Gregory Ewing
greg.ew...@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
On 12 February 2014 10:07, Ben Finney ben+pyt...@benfinney.id.au wrote:
Chris Angelico ros...@gmail.com writes:
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney ben+pyt...@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
Oscar Benjamin oscar.j.benja...@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
Oscar Benjamin oscar.j.benja...@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
On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa ma...@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:
def real_sqrt(y):
for x in continuum(0,
Chris Angelico ros...@gmail.com:
On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa ma...@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
On Fri, Feb 14, 2014 at 6:47 AM, Marko Rauhamaa ma...@pacujo.net 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
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.benja...@gmail.com:
This isn't even a question of resource constraints: a digital computer
with infinite memory and computing power would
Rotwang sg...@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,
On 13/02/2014 22:00, Marko Rauhamaa wrote:
Rotwang sg...@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:
Rotwang sg...@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
--
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,
On Thu, Feb 13, 2014 at 11:47 AM, Marko Rauhamaa ma...@pacujo.net wrote:
Chris Angelico ros...@gmail.com:
On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa ma...@pacujo.net wrote:
Well, if your idealized, infinite, digital computer had ℵ₁ bytes of RAM
and ran at ℵ₁ hertz and Python supported
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 Fri, Feb 14, 2014 at 5:37 PM, Gregory Ewing
greg.ew...@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
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
--
https://mail.python.org/mailman/listinfo/python-list
On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney ben+pyt...@benfinney.id.au wrote:
Chris Angelico ros...@gmail.com writes:
I have yet to find any computer that works with the set of real
numbers in any way. Never mind optimization, they simply cannot work
with real numbers.
Not *any* computer?
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 confuse unicode and
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
Chris Angelico ros...@gmail.com writes:
On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney ben+pyt...@benfinney.id.au
wrote:
Chris Angelico ros...@gmail.com writes:
I have yet to find any computer that works with the set of real
numbers in any way. Never mind optimization, they simply cannot
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney ben+pyt...@benfinney.id.au wrote:
So, if I understand you right, you want to say that you've not found a
computer that works with the *complete* set of real numbers. Yes?
Correct. When jmf referred to real numbers, he implied that there are
no
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 notation
Chris Angelico ros...@gmail.com writes:
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney ben+pyt...@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
On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney ben+pyt...@benfinney.id.au wrote:
Chris Angelico ros...@gmail.com writes:
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney ben+pyt...@benfinney.id.au
wrote:
So, if I understand you right, you want to say that you've not found
a computer that works
The fascinating aspect of this FSR lies
in its mathematical absurdity.
jmf
--
https://mail.python.org/mailman/listinfo/python-list
Chris Angelico ros...@gmail.com writes:
On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney ben+pyt...@benfinney.id.au
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
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
On Wed, Feb 12, 2014 at 10:44 PM, Ben Finney ben+pyt...@benfinney.id.au wrote:
Chris Angelico ros...@gmail.com writes:
On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney ben+pyt...@benfinney.id.au
wrote:
That's why I think you need to be clear that your point isn't
“computers don't work with
Chris Angelico ros...@gmail.com:
Hmm, I'm not sure that my statement is false. If a computer can work
with real numbers, then I would expect it to be able to work with
any real number. In C, I can declare an 'int' variable, which can hold
the real number 4 - does that mean that that variable
On Wed, Feb 12, 2014 at 11:48 PM, Marko Rauhamaa ma...@pacujo.net wrote:
Chris Angelico ros...@gmail.com:
Hmm, I'm not sure that my statement is false. If a computer can work
with real numbers, then I would expect it to be able to work with
any real number. In C, I can declare an 'int'
Chris Angelico ros...@gmail.com:
On Wed, Feb 12, 2014 at 11:48 PM, Marko Rauhamaa ma...@pacujo.net 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
On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote:
Chris Angelico writes:
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote:
So, if I understand you right, you want to say that you've not found
a computer that works with the *complete* set of real numbers. Yes?
On 2014-02-12, Ben Finney ben+pyt...@benfinney.id.au wrote:
Chris Angelico ros...@gmail.com writes:
I have yet to find any computer that works with the set of real
numbers in any way. Never mind optimization, they simply cannot work
with real numbers.
Not *any* computer? Not in *any* way?
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 parse
On Thu, Feb 13, 2014 at 1:13 AM, Marko Rauhamaa ma...@pacujo.net 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
On Wed, Feb 12, 2014 at 7:11 AM, Rustom Mody rustompm...@gmail.com wrote:
On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote:
Chris Angelico writes:
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote:
So, if I understand you right, you want to say that you've not found
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
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
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
Gregory Ewing greg.ew...@canterbury.ac.nz 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
On 2014-02-12, Gregory Ewing greg.ew...@canterbury.ac.nz 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
On Thursday, February 13, 2014 2:15:28 AM UTC+5:30, Ian wrote:
On Wed, Feb 12, 2014 at 7:11 AM, Rustom Mody wrote:
On Wednesday, February 12, 2014 3:37:04 PM UTC+5:30, Ben Finney wrote:
Chris Angelico writes:
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney wrote:
So, if I understand you
On Wed, 12 Feb 2014 21:07:04 +1100, Ben Finney wrote:
Chris Angelico ros...@gmail.com writes:
On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney
ben+pyt...@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
1 - 100 of 102 matches
Mail list logo
