On 2009-Oct-22 17:11:45 -0700, William Stein wrote:
>On Thu, Oct 22, 2009 at 4:52 PM, John H Palmieri
>wrote:
>> First, it's what I've always been taught, and I trust my teachers and
>> professors -- if they were doing something unusual or something about
>> which there was some controversy, the
> From: William Stein
> Date: Thu, 22 Oct 2009 14:14:41 -0700
>
> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri
> wrote:
> >
> >
> >
> > On Oct 22, 8:57 am, William Stein wrote:
> >> On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri
> >> wrote:
> >>
> >> > Anyway, 0^0 is undefined in math
On Oct 22, 2009, at 5:42 PM, John H Palmieri wrote:
>
> On Oct 22, 5:11 pm, William Stein wrote:
>> Well like it or not, it is a fact that 0.0^0.0 = 1 *is* the official
>> ISO 99 standard. Note that ISO = "international standards
>> organization".
>>
>> I'm not making an argument here for or ag
On Oct 22, 6:41 pm, William Stein wrote:
> On Thu, Oct 22, 2009 at 5:42 PM, John H Palmieri
> wrote:
>
> I just mentioned "0^0" to my wife (a Biologist), and she instantly
> said "it doesn't exist".
We could conduct an experiment: survey the UW math department. It's a
little silly so I probab
On Thu, Oct 22, 2009 at 5:42 PM, John H Palmieri wrote:
>
> On Oct 22, 5:11 pm, William Stein wrote:
>> Well like it or not, it is a fact that 0.0^0.0 = 1 *is* the official
>> ISO 99 standard. Note that ISO = "international standards
>> organization".
>>
>> I'm not making an argument here for o
On Oct 23, 12:11 am, John H Palmieri wrote:
> On Oct 22, 1:25 am, Kwankyu Lee wrote:
>
> > Hi,
>
> > The following scares me.
>
> > sage: 0^0
> > 1
> > sage: F.=GF(5)
> > sage: F(0)^0
> > Traceback (most recent call last):
> > ...
> > ArithmeticError: 0^0 is undefined.
>
> > For any x, x^0 is
On Oct 22, 5:11 pm, William Stein wrote:
> Well like it or not, it is a fact that 0.0^0.0 = 1 *is* the official
> ISO 99 standard. Note that ISO = "international standards
> organization".
>
> I'm not making an argument here for or against this. But there is no
> arguing with it being an offici
On Thu, Oct 22, 2009 at 4:52 PM, John H Palmieri wrote:
>
>
>
> On Oct 22, 4:15 pm, Fredrik Johansson
> wrote:
>> On Fri, Oct 23, 2009 at 12:51 AM, John H Palmieri
>>
>>
>>
>>
>>
>> wrote:
>>
>> > On Oct 22, 2:14 pm, William Stein wrote:
>> >> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri
Kwankyu Lee wrote:
> Hi,
>
> The following scares me.
>
> sage: 0^0
> 1
> sage: F.=GF(5)
> sage: F(0)^0
> Traceback (most recent call last):
> ...
> ArithmeticError: 0^0 is undefined.
>
> For any x, x^0 is 1 by definition. Isn't it in Sage? I am using Sage
> 4.1.2
>
>
> Kwankyu
For what it i
On Oct 22, 4:15 pm, Fredrik Johansson
wrote:
> On Fri, Oct 23, 2009 at 12:51 AM, John H Palmieri
>
>
>
>
>
> wrote:
>
> > On Oct 22, 2:14 pm, William Stein wrote:
> >> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri
> >> wrote:
>
> >> > On Oct 22, 8:57 am, William Stein wrote:
> >> >> On
On Thu, Oct 22, 2009 at 4:15 PM, Fredrik Johansson
wrote:
>
> On Fri, Oct 23, 2009 at 12:51 AM, John H Palmieri
> wrote:
>>
>> On Oct 22, 2:14 pm, William Stein wrote:
>>> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri
>>> wrote:
>>>
>>>
>>> > On Oct 22, 8:57 am, William Stein wrote:
>>> >
On Fri, Oct 23, 2009 at 12:51 AM, John H Palmieri
wrote:
>
> On Oct 22, 2:14 pm, William Stein wrote:
>> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri
>> wrote:
>>
>>
>> > On Oct 22, 8:57 am, William Stein wrote:
>> >> On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri
>> >> wrote:
>>
>> >
On Oct 22, 2:14 pm, William Stein wrote:
> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri
> wrote:
>
>
> > On Oct 22, 8:57 am, William Stein wrote:
> >> On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri
> >> wrote:
>
> >> > Anyway, 0^0 is undefined in mathematics, so it's good that it's
> >
On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri wrote:
>
>
>
> On Oct 22, 8:57 am, William Stein wrote:
>> On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri
>> wrote:
>>
>> > Anyway, 0^0 is undefined in mathematics, so it's good that it's
>> > undefined in Sage.
>>
>> It's defined for Sage *in
On Oct 22, 8:57 am, William Stein wrote:
> On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri
> wrote:
>
> > Anyway, 0^0 is undefined in mathematics, so it's good that it's
> > undefined in Sage.
>
> It's defined for Sage *integers*:
>
> sage: 0^0
> 1
What about:
sage: 0.000^0.000
1.0
On Oct 22, 2009, at 3:03 PM, Francis Clarke wrote:
The following article has interesting remarks on this question,
particularly pages 407--408:
\bib{MR1163629}{article}{
author={Knuth, Donald E.},
title={Two notes on notation},
journal={Amer. Math. Monthly},
volume={99},
date={1992}
The following article has interesting remarks on this question,
particularly pages 407--408:
\bib{MR1163629}{article}{
author={Knuth, Donald E.},
title={Two notes on notation},
journal={Amer. Math. Monthly},
volume={99},
date={1992},
number={5},
pages={403--422},
}
Among the
>>> For any x, x^0 is 1 by definition.
>>
>> I always thought that for any y, 0^y = 0.
>>
>> Anyway, 0^0 is undefined in mathematics, so it's good that it's
>> undefined in Sage.
>
> It's defined for Sage *integers*:
...
I think I've seen this discussion before. Categories!
Martin
--~--~-
About 0^0
> Even for discrete things like elements of GF(5)? I haven't thought
> about what 0^0 is for things where the continuous limit doesn't make sense.
>
In any ring, integer power x^n is défined by x^0 = 1, because an empty
product is the unit element.
The reason is the same for 0!=1.
John H Palmieri wrote:
>
>
> On Oct 22, 1:25 am, Kwankyu Lee wrote:
>> Hi,
>>
>> The following scares me.
>>
>> sage: 0^0
>> 1
>> sage: F.=GF(5)
>> sage: F(0)^0
>> Traceback (most recent call last):
>> ...
>> ArithmeticError: 0^0 is undefined.
>>
>> For any x, x^0 is 1 by definition.
>
> I alw
On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri wrote:
>
>
>
> On Oct 22, 1:25 am, Kwankyu Lee wrote:
>> Hi,
>>
>> The following scares me.
>>
>> sage: 0^0
>> 1
>> sage: F.=GF(5)
>> sage: F(0)^0
>> Traceback (most recent call last):
>> ...
>> ArithmeticError: 0^0 is undefined.
>>
>> For any x,
On Oct 22, 1:25 am, Kwankyu Lee wrote:
> Hi,
>
> The following scares me.
>
> sage: 0^0
> 1
> sage: F.=GF(5)
> sage: F(0)^0
> Traceback (most recent call last):
> ...
> ArithmeticError: 0^0 is undefined.
>
> For any x, x^0 is 1 by definition.
I always thought that for any y, 0^y = 0. :)
Anyw
On 8/28/07, Stephen Forrest <[EMAIL PROTECTED]> wrote:
> On 8/28/07, William Stein <[EMAIL PROTECTED]> wrote:
> >
> > In SAGE until now 0^0 gave 1 as answer. We are almost certainly going to
> > change
> > this to raise an ArithmeticError. Does anybody have any strong
> > feelings about this?
>
On 8/28/07, Kyle Schalm <[EMAIL PROTECTED]> wrote:
>
>
> as long as the polynomial x^0 continues to evaluate to 1 at x=0, i'm happy
> with defining 0^0 to be whatever.
Well, suppose that were the case. What then should the expression
0^x evaluate to at x=0?
Steve
--~--~-~--~~-
On 8/28/07, William Stein <[EMAIL PROTECTED]> wrote:
>
> In SAGE until now 0^0 gave 1 as answer. We are almost certainly going to
> change
> this to raise an ArithmeticError. Does anybody have any strong
> feelings about this?
> By the way, Magma, PARI, Gap, and Maple all give 1 as the output f
as long as the polynomial x^0 continues to evaluate to 1 at x=0, i'm happy
with defining 0^0 to be whatever.
On Tue, 28 Aug 2007, William Stein wrote:
>
> Hi,
>
> In SAGE until now 0^0 gave 1 as answer. We are almost certainly going to
> change
> this to raise an ArithmeticError. Does anybo
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