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 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 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 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
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
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
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
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
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? The Python built-in ‘float’ type
“works with the set of real
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
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
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
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