Re: Is zero even or odd?

From: Dave Seaman (dseaman_at_no.such.host)
Date: 12/28/04 

Date: Tue, 28 Dec 2004 18:21:18 +0000 (UTC)

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.

> (-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). 

-- 
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>

Relevant Pages

  • Re: Is zero even or odd?
    ... >> from the empty set to itself. ... using about half a dozen or so different C compilers on various platforms, ... The Macintosh calculator returns 1. ... Dave Seaman ...
    (sci.electronics.design)
  • Re: Is zero even or odd?
    ... >> from the empty set to itself. ... using about half a dozen or so different C compilers on various platforms, ... The Macintosh calculator returns 1. ... Dave Seaman ...
    (sci.physics)
  • Re: Is zero even or odd?
    ... >> from the empty set to itself. ... using about half a dozen or so different C compilers on various platforms, ... The Macintosh calculator returns 1. ... Dave Seaman ...
    (sci.astro)
  • Re: Is zero even or odd?
    ... >> from the empty set to itself. ... using about half a dozen or so different C compilers on various platforms, ... The Macintosh calculator returns 1. ... Dave Seaman ...
    (sci.math)
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