[25339] in Perl-Users-Digest
Perl-Users Digest, Issue: 7584 Volume: 10
daemon@ATHENA.MIT.EDU (Perl-Users Digest)
Tue Dec 28 14:10:54 2004
Date: Tue, 28 Dec 2004 11:10:20 -0800 (PST)
From: Perl-Users Digest <Perl-Users-Request@ruby.OCE.ORST.EDU>
To: Perl-Users@ruby.OCE.ORST.EDU (Perl-Users Digest)
Perl-Users Digest Tue, 28 Dec 2004 Volume: 10 Number: 7584
Today's topics:
Re: how Encode::Hanextra work? <chaoslawful@gmail.com>
Re: how to delete files that create date <=20041210 <bik.mido@tiscalinet.it>
Re: Is zero even or odd? <nospam@nospam.com>
Re: Is zero even or odd? <hadrainc@earthlink.net>
Re: Is zero even or odd? <hadrainc@earthlink.net>
Re: Is zero even or odd? <hadrainc@earthlink.net>
Re: Is zero even or odd? <hadrainc@earthlink.net>
Re: Is zero even or odd? (Matthew Russotto)
Re: Is zero even or odd? <dseaman@no.such.host>
Re: Is zero even or odd? <krw@att.bizzzz>
Re: Is zero even or odd? <jmw@jmwa.demon.contraspam.yuk>
Re: Is zero even or odd? <jfields@austininstruments.com>
Re: Is zero even or odd? <dseaman@no.such.host>
Re: Is zero even or odd? <dseaman@no.such.host>
Re: Is zero even or odd? <a.newmane.remove@eastcoastcz.com>
Re: Is zero even or odd? <a.newmane.remove@eastcoastcz.com>
Re: Is zero even or odd? <matternc@comcast.net>
Re: Is zero even or odd? <a.newmane.remove@eastcoastcz.com>
Re: Is zero even or odd? <jmw@jmwa.demon.contraspam.yuk>
Re: Is zero even or odd? <jmw@jmwa.demon.contraspam.yuk>
Re: Is zero even or odd? <dseaman@no.such.host>
Re: Is zero even or odd? <a.newmane.remove@eastcoastcz.com>
Digest Administrivia (Last modified: 6 Apr 01) (Perl-Users-Digest Admin)
----------------------------------------------------------------------
Date: Wed, 29 Dec 2004 00:23:35 +0800
From: chaoslawful <chaoslawful@gmail.com>
Subject: Re: how Encode::Hanextra work?
Message-Id: <cqs1fg$1lqf$1@mail.cn99.com>
ke.kewen@gmail.com wrote:
> I use ActivePerl 5.8.6, and install the Encode::Hanextra module through
> PPM, but the perl couldn't find the codepage of "gb18030".
>
> I find the next three lines in Encode\Config.pm:
> #'big5plus' => 'Encode::HanExtra',
> #'euc-tw' => 'Encode::HanExtra',
> #'gb18030' => 'Encode::HanExtra',
> after un-comment these lines. "gb18030" could work, but the alias
> "GB-18030" couldn't work.
> Is there some bug? or I do something wrong?
> Thanks very much.
>
It seems that the aliases are only defined in Encode::HanExtra, so you
have to "use Encode::HanExtra;".
------------------------------
Date: Tue, 28 Dec 2004 17:17:29 +0100
From: Michele Dondi <bik.mido@tiscalinet.it>
Subject: Re: how to delete files that create date <=20041210
Message-Id: <mj13t0lhmvknpjuet0mr030ltsq7ghdv30@4ax.com>
On Mon, 27 Dec 2004 16:16:53 GMT, "Paul Lalli" <mritty@gmail.com>
wrote:
>use strict;
>use warnings;
[snip]
>Please read:
>perldoc -q quoting
>
>No reason to make assignments to all those variables if you're not going
>to use them:
>my $ctime = (stat($a))[10];
Oh, and while we're there let's remind him that it's better to avoid
using $a and $b as general purpose variables. (To the OP: see 'perldoc
perlvar'.)
Michele
--
{$_=pack'B8'x25,unpack'A8'x32,$a^=sub{pop^pop}->(map substr
(($a||=join'',map--$|x$_,(unpack'w',unpack'u','G^<R<Y]*YB='
.'KYU;*EVH[.FHF2W+#"\Z*5TI/ER<Z`S(G.DZZ9OX0Z')=~/./g)x2,$_,
256),7,249);s/[^\w,]/ /g;$ \=/^J/?$/:"\r";print,redo}#JAPH,
------------------------------
Date: Tue, 28 Dec 2004 14:25:35 GMT
From: Fred Bloggs <nospam@nospam.com>
Subject: Re: Is zero even or odd?
Message-Id: <41D16C8A.7050103@nospam.com>
George Cox wrote:
> Fred Bloggs wrote:
>
>>Apparently you can't pick up on "0/0" being a symbol- call it @#$%^&*,
>>which has been shown to be the set of all numbers.
>
>
> Are you claiming that
>
> 0/0 = set of all numbers
>
> ? Because if you are you are wrong.
Ookay- thnx for the insight.
------------------------------
Date: Tue, 28 Dec 2004 15:19:11 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <flt2t0tr0brtnee6m51sibk9hfj793cf9p@4ax.com>
On Mon, 27 Dec 2004 20:58:35 -0600, russotto@grace.speakeasy.net
(Matthew Russotto) wrote:
>Well, 0^0 is a mess. But lim x->0 0^x is well defined.
Two entirely different expressions. N^0=1, N can't be 0.
0^n = 0, n can't be 0. limit if n->0 of 0^n is meaningless. 0 is a
`place holder between 1 and -1, it can only participate in addition,
subtraction, and multiplication; and calculus notation where it is
used to identify instantaneous rates.
------------------------------
Date: Tue, 28 Dec 2004 15:20:30 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <vcu2t09h6l61ic154seo11f3vihqqe9kf9@4ax.com>
On Tue, 28 Dec 2004 04:56:23 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> wrote:
>No, it isn't. That limit does not exist.
>But 0^0 does exist and has nothing to do with limits.
>
Only in your mind.
------------------------------
Date: Tue, 28 Dec 2004 15:25:30 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <fju2t0l5ds6mhv4uampdfbj5hjjdf223j2@4ax.com>
On Tue, 28 Dec 2004 10:19:37 -0000, "George Dishman"
<george@briar.demon.co.uk> wrote:
>Generally resistance varies with temperature
And a few other conditions. But true, resistance varies with
temperature (and other factors) which open the path to
superconductivity.
------------------------------
Date: Tue, 28 Dec 2004 15:30:21 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <5qu2t0hhvbisgdp42rd7cuaf8ua8v75h57@4ax.com>
On Tue, 28 Dec 2004 05:55:17 -0600, John Fields
<jfields@austininstruments.com> wrote:
>Very nice.
>
>For the normal order of precedence, my argument is that in order for
>x/x = 1 to be true, the numerator and the denominator must both be
>equal at the time of the division. That is, for any set of x's where
>x = x, x/x = 1. If that's true, and 0 = 0, then 0/0 must be equal to
>1. The proof is the proof of exhaustion.
Sound of spinning wheels, Return to the first math course that refers
to division that you ever took. Note one of the original laws:
`division by 0 is undefined and meaningless'. period, over, and out.
------------------------------
Date: Tue, 28 Dec 2004 09:46:05 -0600
From: russotto@grace.speakeasy.net (Matthew Russotto)
Subject: Re: Is zero even or odd?
Message-Id: <jI-dnU8kDuog4kzcRVn-rw@speakeasy.net>
In article <cqqp1n$rgb$2@mailhub227.itcs.purdue.edu>,
Dave Seaman <dseaman@no.such.host> wrote:
>On Mon, 27 Dec 2004 20:58:35 -0600, Matthew Russotto wrote:
>> In article <t4rss0duo9eho2urcsibtq302e3s3edqkr@4ax.com>,
>> vonroach <hadrainc@earthlink.net> wrote:
>>>On Fri, 24 Dec 2004 19:46:25 GMT, "Nicholas O. Lindan" <see@sig.com>
>>>wrote:
>>>
>>>>0^0 is a mess in either system.
>>>
>>>A meaningless mess. As Pauli might say `it isn't even wrong'. And
>>>Heisenberg would add a `pile of crap'.
>
>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
>
>No, it isn't. That limit does not exist.
Most certainly does. It's zero.
>But 0^0 does exist and has nothing to do with limits.
0^0 can be defined by convention, of course, as is 0 factorial.
------------------------------
Date: Tue, 28 Dec 2004 16:09:56 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 09:46:05 -0600, Matthew Russotto wrote:
> In article <cqqp1n$rgb$2@mailhub227.itcs.purdue.edu>,
> Dave Seaman <dseaman@no.such.host> wrote:
>>On Mon, 27 Dec 2004 20:58:35 -0600, Matthew Russotto wrote:
>>> In article <t4rss0duo9eho2urcsibtq302e3s3edqkr@4ax.com>,
>>> vonroach <hadrainc@earthlink.net> wrote:
>>>>On Fri, 24 Dec 2004 19:46:25 GMT, "Nicholas O. Lindan" <see@sig.com>
>>>>wrote:
>>>>
>>>>>0^0 is a mess in either system.
>>>>
>>>>A meaningless mess. As Pauli might say `it isn't even wrong'. And
>>>>Heisenberg would add a `pile of crap'.
>>
>>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
>>
>>No, it isn't. That limit does not exist.
> Most certainly does. It's zero.
Wrong. That limit cannot exist because 0^x is undefined for all x < 0.
>>But 0^0 does exist and has nothing to do with limits.
> 0^0 can be defined by convention, of course, as is 0 factorial.
I consider it to be something more than a mere convention. In Suppes:
_Axiomatic Set Theory_, it's a *theorem* that m^0 = 1 for every cardinal
m. Since 0 is a cardinal, the corollary is that 0^0 = 1. Specifically,
it represents the cardinality of the set of mappings from the empty set
to itself.
A corollary is the very antithesis of a "convention."
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 11:31:17 -0500
From: Keith Williams <krw@att.bizzzz>
Subject: Re: Is zero even or odd?
Message-Id: <MPG.1c3b54649eb3f7269897ff@news.individual.net>
In article <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>,
dseaman@no.such.host says...
> On Tue, 28 Dec 2004 09:46:05 -0600, Matthew Russotto wrote:
> > In article <cqqp1n$rgb$2@mailhub227.itcs.purdue.edu>,
> > Dave Seaman <dseaman@no.such.host> wrote:
> >>On Mon, 27 Dec 2004 20:58:35 -0600, Matthew Russotto wrote:
> >>> In article <t4rss0duo9eho2urcsibtq302e3s3edqkr@4ax.com>,
> >>> vonroach <hadrainc@earthlink.net> wrote:
> >>>>On Fri, 24 Dec 2004 19:46:25 GMT, "Nicholas O. Lindan" <see@sig.com>
> >>>>wrote:
> >>>>
> >>>>>0^0 is a mess in either system.
> >>>>
> >>>>A meaningless mess. As Pauli might say `it isn't even wrong'. And
> >>>>Heisenberg would add a `pile of crap'.
> >>
> >>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
> >>
> >>No, it isn't. That limit does not exist.
>
> > Most certainly does. It's zero.
>
> Wrong. That limit cannot exist because 0^x is undefined for all x < 0.
"lim x->0 0^x "
Where is X < 0 in the above?
--
Keith
------------------------------
Date: Tue, 28 Dec 2004 16:35:39 +0000
From: John Woodgate <jmw@jmwa.demon.contraspam.yuk>
Subject: Re: Is zero even or odd?
Message-Id: <Y63zIODbtY0BFw$j@jmwa.demon.co.uk>
I read in sci.electronics.design that Dave Seaman <dseaman@no.such.host>
wrote (in <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>) about 'Is zero even
or odd?', on Tue, 28 Dec 2004:
>That limit cannot exist because 0^x is undefined for all x < 0.
'Undefined' is a human artefact. ANYTHING can be defined; if it's badly
defined, the definition may cause a contradiction.
In this case, the nature of negative powers of 0 does not affect the
limit, as x tends to 0 from positive values, of x^0. Now, are there any
grounds for supposing (or even proving) that the limit, as x tends to 0
from positive values, of 0^x differs from the above limit value?
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
------------------------------
Date: Tue, 28 Dec 2004 11:05:22 -0600
From: John Fields <jfields@austininstruments.com>
Subject: Re: Is zero even or odd?
Message-Id: <l923t010un0jr7i9m5f4g5i64r583i077s@4ax.com>
On Tue, 28 Dec 2004 15:30:21 GMT, vonroach <hadrainc@earthlink.net>
wrote:
>On Tue, 28 Dec 2004 05:55:17 -0600, John Fields
><jfields@austininstruments.com> wrote:
>
>>Very nice.
>>
>>For the normal order of precedence, my argument is that in order for
>>x/x = 1 to be true, the numerator and the denominator must both be
>>equal at the time of the division. That is, for any set of x's where
>>x = x, x/x = 1. If that's true, and 0 = 0, then 0/0 must be equal to
>>1. The proof is the proof of exhaustion.
>
>Sound of spinning wheels, Return to the first math course that refers
>to division that you ever took. Note one of the original laws:
>`division by 0 is undefined and meaningless'. period, over, and out.
---
How comforting it must be for you to know that somewhere, on a dusty
old bookrack, lies a little book which releases you from the drudgery
of thinking.
--
John Fields
------------------------------
Date: Tue, 28 Dec 2004 17:25:57 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 11:31:17 -0500, Keith Williams wrote:
> In article <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>,
> dseaman@no.such.host says...
>> >>
>> >>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
>> >>
>> >>No, it isn't. That limit does not exist.
>>
>> > Most certainly does. It's zero.
>>
>> Wrong. That limit cannot exist because 0^x is undefined for all x < 0.
> "lim x->0 0^x "
> Where is X < 0 in the above?
Look up the definition of limit. Notice that "limit" in the reals means
"two-sided limit." In particular, that means the left-hand and
right-hand limits must both exist, and must agree.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 17:38:31 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqs5mn$j1c$2@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 16:35:39 +0000, John Woodgate wrote:
> I read in sci.electronics.design that Dave Seaman <dseaman@no.such.host>
> wrote (in <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>) about 'Is zero even
> or odd?', on Tue, 28 Dec 2004:
>>That limit cannot exist because 0^x is undefined for all x < 0.
> 'Undefined' is a human artefact. ANYTHING can be defined; if it's badly
> defined, the definition may cause a contradiction.
There is no way to define 0^x for negative x such that the laws of
exponents are preserved.
> In this case, the nature of negative powers of 0 does not affect the
> limit, as x tends to 0 from positive values, of x^0. Now, are there any
> grounds for supposing (or even proving) that the limit, as x tends to 0
> from positive values, of 0^x differs from the above limit value?
Then you don't know the definition of limit. In the case of real
functions, it goes like this:
Definition. Let f: D -> R, where D is a subset of the reals,
and let L be a real number. Given a in D, we say lim_{x->a} f(x)
= L if, for every epsilon > 0, there exists delta > 0 such that
0 < |x-a| < delta => |f(x) - L| < epsilon. (*)
Compare this with the definition of the right-hand limit:
Definition. Let f: D -> R, where D is a subset of the reals,
and let L be a real number. Given a in D, we say lim_{x->a+} f(x)
= L if, for every epsilon > 0, there exists delta > 0 such that
0 < x-a < delta => |f(x) - L| < epsilon. (**)
Notice the crucial difference between (*) and (**), where |x-a| is
replaced by x-a. The (**) condition requires x to be greater than a, but
(*) allows x to be on either side of a, as long as it is suitably close.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 09:44:55 -0800
From: "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com>
Subject: Re: Is zero even or odd?
Message-Id: <33dkcrF3v903uU1@individual.net>
vonroach wrote:
> On Tue, 28 Dec 2004 04:56:23 +0000 (UTC), Dave Seaman
> <dseaman@no.such.host> wrote:
>
>> No, it isn't. That limit does not exist.
>> But 0^0 does exist and has nothing to do with limits.
>>
> Only in your mind.
Here you go again.
0^0 is undefined.
------------------------------
Date: Tue, 28 Dec 2004 09:51:12 -0800
From: "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com>
Subject: Re: Is zero even or odd?
Message-Id: <33dkokF3vfnfcU1@individual.net>
Dave Seaman wrote:
> On Tue, 28 Dec 2004 09:46:05 -0600, Matthew Russotto wrote:
>> In article <cqqp1n$rgb$2@mailhub227.itcs.purdue.edu>,
>> Dave Seaman <dseaman@no.such.host> wrote:
>>> On Mon, 27 Dec 2004 20:58:35 -0600, Matthew Russotto wrote:
>>>> In article <t4rss0duo9eho2urcsibtq302e3s3edqkr@4ax.com>,
>>>> vonroach <hadrainc@earthlink.net> wrote:
>>>>> On Fri, 24 Dec 2004 19:46:25 GMT, "Nicholas O. Lindan"
>>>>> <see@sig.com> wrote:
>>>>>
>>>>>> 0^0 is a mess in either system.
>>>>>
>>>>> A meaningless mess. As Pauli might say `it isn't even wrong'. And
>>>>> Heisenberg would add a `pile of crap'.
>>>
>>>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
>>>
>>> No, it isn't. That limit does not exist.
>
>> Most certainly does. It's zero.
>
> Wrong. That limit cannot exist because 0^x is undefined for all x <
> 0.
>
>>> But 0^0 does exist and has nothing to do with limits.
>
>> 0^0 can be defined by convention, of course, as is 0 factorial.
>
> 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)
(-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.
------------------------------
Date: Tue, 28 Dec 2004 12:51:42 -0500
From: Chris Mattern <matternc@comcast.net>
Subject: Re: Is zero even or odd?
Message-Id: <nP-dnbK8M6ezAEzcRVn-ig@comcast.com>
Keith Williams wrote:
>
> "lim x->0 0^x "
>
> Where is X < 0 in the above?
>
For a limit of a function to be evaluated
at a specific number, you must be
able to define the function on an open
interval *around* the number (except
possibly at the number itself); i.e., you
must be able define the function for values
both greater than and less than the number.
*That's* where x < 0 in the above.
--
Christopher Mattern
"Which one you figure tracked us?"
"The ugly one, sir."
"...Could you be more specific?"
------------------------------
Date: Tue, 28 Dec 2004 09:57:20 -0800
From: "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com>
Subject: Re: Is zero even or odd?
Message-Id: <33dl43F3v97sjU1@individual.net>
vonroach wrote:
> On Mon, 27 Dec 2004 20:58:35 -0600, russotto@grace.speakeasy.net
> (Matthew Russotto) wrote:
>
>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
>
> Two entirely different expressions. N^0=1, N can't be 0.
> 0^n = 0, n can't be 0.
Actually, for 0^n = 0, n has to be greator than 0, as it cannot be
negative too.
the valid DOMAIN for 0^n is anything greator than 0. ) and anything
below (that is, negative) are out of the domain, and therefore, invalid.
------------------------------
Date: Tue, 28 Dec 2004 18:13:29 +0000
From: John Woodgate <jmw@jmwa.demon.contraspam.yuk>
Subject: Re: Is zero even or odd?
Message-Id: <KZTHAXEJJa0BFweJ@jmwa.demon.co.uk>
I read in sci.electronics.design that Dave Seaman <dseaman@no.such.host>
wrote (in <cqs5mn$j1c$2@mailhub227.itcs.purdue.edu>) about 'Is zero even
or odd?', on Tue, 28 Dec 2004:
>Then you don't know the definition of limit.
You just want to win the argument, come what may. It is very clear from
my post that I invoked the right-hand limit. You didn't event attempt to
deal with my proposition but accused me of ignorance of a concept that I
did not use in my proposition.
I will not discuss with you any more.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
------------------------------
Date: Tue, 28 Dec 2004 18:14:54 +0000
From: John Woodgate <jmw@jmwa.demon.contraspam.yuk>
Subject: Re: Is zero even or odd?
Message-Id: <Ep2EciEeKa0BFw97@jmwa.demon.co.uk>
I read in sci.electronics.design that Alfred Z. Newmane <a.newmane.remov
e@eastcoastcz.com> wrote (in <33dkokF3vfnfcU1@individual.net>) about 'Is
zero even or odd?', on Tue, 28 Dec 2004:
>I've checked every calc I could find with a power function to verify
>this. Any graphing type calc yeilds some sort of DOMAIN error, and any
>sci calc I've tried simply gives a generic error.
Could it be that we are discussing pure mathematics, not calculators, or
Ohm's Law, or the price of imaginary apples?
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
------------------------------
Date: Tue, 28 Dec 2004 18:21:18 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqs86u$kjb$1@mailhub227.itcs.purdue.edu>
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>
------------------------------
Date: Tue, 28 Dec 2004 10:29:36 -0800
From: "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com>
Subject: Re: Is zero even or odd?
Message-Id: <33dn0jF3vhjtjU1@individual.net>
John Woodgate wrote:
> I read in sci.electronics.design that Alfred Z. Newmane
> <a.newmane.remov e@eastcoastcz.com> wrote (in
> <33dkokF3vfnfcU1@individual.net>) about 'Is zero even or odd?', on
> Tue, 28 Dec 2004:
>> 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.
>
> Could it be that we are discussing pure mathematics, not calculators,
> or Ohm's Law, or the price of imaginary apples?
I was using to prove a point of pure mathematics, that 0^0 is undefined
(out of the valid domain.)
------------------------------
Date: 6 Apr 2001 21:33:47 GMT (Last modified)
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End of Perl-Users Digest V10 Issue 7584
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