On Fri, 09 Jan 2015 19:57:20 -0800, Devin Jeanpierre wrote:
On Fri, Jan 9, 2015 at 7:05 PM, Gregory Ewing
greg.ew...@canterbury.ac.nz wrote:
It's far from clear what *anything* multiplied by itself zero times
should be.
A better way of thinking about what x**n for integer n means is this:
Steven D'Aprano wrote:
I'm just sketching an informal proof. If you want to make it vigorous
I think the usual term is rigorous, unless the mathematician
is taking some kind of stimulant... :-)
--
Greg
--
Steven D'Aprano wrote:
Arguably, *integer* 0**0 could be zero, on the basis that you can't take
limits of integer-valued quantities, and zero times itself zero times
surely has to be zero.
It's far from clear what *anything* multiplied by
itself zero times should be.
A better way of thinking
On Fri, Jan 9, 2015 at 2:20 AM, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info wrote:
-snip-
I don't understand what you're trying to say here. You can't just
arbitrarily declare that 0**1 equals something other than 0 (or for that
matter, doesn't equal anything at all).
You can,
On Fri, Jan 9, 2015 at 7:05 PM, Gregory Ewing
greg.ew...@canterbury.ac.nz wrote:
It's far from clear what *anything* multiplied by
itself zero times should be.
A better way of thinking about what x**n for integer
n means is this: Start with 1, and multiply it by
x n times. The result of this
Devin Jeanpierre wrote:
On Thu, Jan 8, 2015 at 6:43 PM, Dave Angel da...@davea.name wrote:
What you don't say is which behavior you actually expected. Since 0**0
is undefined mathematically, I'd expect either an exception or a NAN
result.
It can be undefined, if you choose for it to be.
Marko, your argument is this function x**y(a, x) must be continuous
on [0, inf), and to be continuous at 0, 0**0 must be a. Since there
are many possible values of a, this is not a justification, this is
a proof by contradiction that the premise was faulty: x**y(a, x)
doesn't have to be continuous
Devin Jeanpierre writes:
[...]
domain of the natural numbers. Knuth says that thought of
combinatorially on the naturals, x**y counts the number of mappings
from a set of x values to a set of y values.
It's the other way around, of course: from a set of y values to a set
of x values.
Which
Chris Angelico ros...@gmail.com:
I'm not a mathematical expert, so I don't quite 'get' this. How does
this justify 0**0 being equal to 0.5?
Many operations like this are defined in terms of some very strong
argument of uniqueness. Ultimately, the key point is safety in
mathematical deductions.
Steven D'Aprano steve+comp.lang.pyt...@pearwood.info:
Devin Jeanpierre wrote:
No you can't -- that would make arithmetic inconsistent. 0**1 is
perfectly well defined as 0 however you look at it:
You *could* leave 0**1 undefined. You *could* leave 7+0 undefined.
However, that would make
I think we're in violent agreement here, nevertheless I think you're right
for the wrong reasons. See below...
Devin Jeanpierre wrote:
On Fri, Jan 9, 2015 at 12:49 AM, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info wrote:
Devin Jeanpierre wrote:
On Thu, Jan 8, 2015 at 6:43 PM, Dave
On Fri, Jan 9, 2015 at 12:58 AM, Devin Jeanpierre
jeanpierr...@gmail.com wrote:
Arguably, *integer* 0**0 could be zero, on the basis that you can't take
limits of integer-valued quantities, and zero times itself zero times
surely has to be zero.
I should have responded in more detail here,
Steven D'Aprano steve+comp.lang.pyt...@pearwood.info:
mathematicians with a pragmatic bent
You shouldn't call engineers and scientists mathematicians (with a
pragmatic bent). Rigor is an absolute requirement for any mathematics.
Marko
--
https://mail.python.org/mailman/listinfo/python-list
On Fri, Jan 9, 2015 at 12:49 AM, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info wrote:
Devin Jeanpierre wrote:
On Thu, Jan 8, 2015 at 6:43 PM, Dave Angel da...@davea.name wrote:
What you don't say is which behavior you actually expected. Since 0**0
is undefined mathematically, I'd
On Fri, Jan 9, 2015 at 9:20 PM, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info wrote:
On the basis that m**n means m multiplied by itself n times:
5**4 = 5*5*5*5 = 625
that gives us:
0**0 = zero multiplied by itself zero times.
You can multiply 0 by any number you like, and the
Marko Rauhamaa wrote:
Steven D'Aprano steve+comp.lang.pyt...@pearwood.info:
mathematicians with a pragmatic bent
You shouldn't call engineers and scientists mathematicians (with a
pragmatic bent). Rigor is an absolute requirement for any mathematics.
I wasn't referring to engineers,
I want to emphasis that I'm not really arguing that 0**0 should evaluate as
0. That's probably the least useful thing we can have out of the four
possibilities:
- return 1
- return NAN
- raise an exception
- return 0
But in the spirit of the Devil's Advocate, I mentioned that there was an
On Fri, Jan 9, 2015 at 11:24 PM, Steven D'Aprano
steve+comp.lang.pyt...@pearwood.info wrote:
5 * 0 * 0 * 0 * 0 = 0
Where did the 5 come from?
You're effectively saying that 0**0 becomes 5*0**0, then cancelling the 0**0
because they're all zeroes and so don't matter, leaving 5. And that
On Thu, Jan 8, 2015 at 6:33 PM, Devin Jeanpierre jeanpierr...@gmail.com wrote:
I noticed some very PHP-ish behavior today:
import decimal
x = 0
y = float(x)
z = decimal.Decimal(x)
x == y == z == x
True
x ** x
1
y**y
1.0
z**z
Traceback (most recent call last):
File stdin, line 1,
On Thu, Jan 8, 2015 at 6:43 PM, Dave Angel da...@davea.name wrote:
What you don't say is which behavior you actually expected. Since 0**0 is
undefined mathematically, I'd expect either an exception or a NAN result.
It can be undefined, if you choose for it to be. You can also choose
to not
Thanks Ben, with your encouragement I have filed
http://bugs.python.org/issue23201
-- Devin
On Thu, Jan 8, 2015 at 7:03 PM, Ben Finney ben+pyt...@benfinney.id.au wrote:
Dave Angel da...@davea.name writes:
What you don't say is which behavior you actually expected. Since
0**0 is undefined
I noticed some very PHP-ish behavior today:
import decimal
x = 0
y = float(x)
z = decimal.Decimal(x)
x == y == z == x
True
x ** x
1
y**y
1.0
z**z
Traceback (most recent call last):
File stdin, line 1, in module
File /usr/lib/python2.7/decimal.py, line 2216, in __pow__
return
Dave Angel da...@davea.name writes:
What you don't say is which behavior you actually expected. Since
0**0 is undefined mathematically, I'd expect either an exception or a
NAN result.
Do you think that the ‘int’ and ‘float’ types, which do produce a number
result for ‘0 ** 0’, are buggy and
On 01/08/2015 09:33 PM, Devin Jeanpierre wrote:
I noticed some very PHP-ish behavior today:
import decimal
x = 0
y = float(x)
z = decimal.Decimal(x)
x == y == z == x
True
x ** x
1
y**y
1.0
z**z
Traceback (most recent call last):
File stdin, line 1, in module
File
Dave Angel da...@davea.name:
What you don't say is which behavior you actually expected. Since 0**0
is undefined mathematically, I'd expect either an exception or a NAN
result.
IEEE 754 mandates that 0**0 should evaluate to 1:
URL:
On 01/09/2015 02:37 AM, Chris Angelico wrote:
On Fri, Jan 9, 2015 at 6:28 PM, Marko Rauhamaa ma...@pacujo.net wrote:
Devin Jeanpierre jeanpierr...@gmail.com:
If 0**0 is defined, it must be 1.
You can justify any value a within [0, 1]. For example, choose
y(a, x) = log(a, x)
Then,
Devin Jeanpierre jeanpierr...@gmail.com:
If 0**0 is defined, it must be 1.
You can justify any value a within [0, 1]. For example, choose
y(a, x) = log(a, x)
Then,
limy(a, x) = 0
x - 0+
and:
lim[x - 0+] x**y(a, x) = a
For example,
a = 0.5
x = 1e-100
y =
On Fri, Jan 9, 2015 at 6:28 PM, Marko Rauhamaa ma...@pacujo.net wrote:
Devin Jeanpierre jeanpierr...@gmail.com:
If 0**0 is defined, it must be 1.
You can justify any value a within [0, 1]. For example, choose
y(a, x) = log(a, x)
Then,
limy(a, x) = 0
x - 0+
and:
Devin Jeanpierre jeanpierr...@gmail.com writes:
decimal.InvalidOperation: 0 ** 0
I'd file a bug report but I'm anticipating some rational (heh)
explanation. Any ideas?
First note that it's explicitly documented as an invalid operation
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