Re: Is zero even or odd?
From: Alfred Z. Newmane (a.newmane.remove_at_eastcoastcz.com)
Date: 12/28/04
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Date: Tue, 28 Dec 2004 11:15:07 -0800
Dave Seaman wrote:
> On Tue, 28 Dec 2004 09:51:12 -0800, Alfred Z. Newmane wrote:
>> Dave Seaman wrote:
>>>
>>> I consider it to be something more than a mere convention. In
>>> Suppes: _Axiomatic Set Theory_, it's a *theorem* that m^0 = 1 for
>>> every cardinal m. Since 0 is a cardinal, the corollary is that 0^0
>>> = 1. Specifically, it represents the cardinality of the set of
>>> mappings from the empty set to itself.
>>>
>>> A corollary is the very antithesis of a "convention."
>
>> .
>> .
>> .
>> 2^0 = 1
>> 1^0 = 1
>> 0^0 = ERROR, DOMAIN (hence the limit)
>
> Says who? I just compiled and ran the following C program
>
> -------------------------------
> #include <math.h>
> #include <stdio.h>
>
> int main(int argc, char **argv)
> {
> printf("%f\n", pow(0,0));
> return 0;
> }
> -------------------------------
>
> using about half a dozen or so different C compilers on various
> platforms, and every single one of them printed 1.000000. Similarly
> for most other programming languages that I have tried. However, the
> mathematical definition says what it says regardless of whether
> computer implementations happen to get it right or not.
Curious enough, C, C++, Java (1.4.2_01) and Perl (5.6.1) all return 1,
as does the windows calc, and the "Simple Calculator" on my Linux
system.
But correct me if I'm wrong, isn't returning 1 from 0^0 /mathematically/
incorrect? I have always known that to be out of the valid domain for
n^0.
>> (-1)^0 = 1
>> (-2)^0 = 1
>> .
>> .
>> .
>
>> I've checked every calc I could find with a power function to verify
>> this. Any graphing type calc yeilds some sort of DOMAIN error, and
>> any sci calc I've tried simply gives a generic error.
>
> The Macintosh calculator returns 1. So do most Hewlett-Packard
> calculators that I have tried, and at least one by Texas Instruments
> that I can recall. Likewise Maple and MATLAB (but not Mathematica).
Guess it depends on when the calc was made (and perhaps who made it.) I
tested on both a TI86 (graphing) and TI36x (sci) for TI calcs ,bothing
giving errors.
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