[25342] in Perl-Users-Digest
Perl-Users Digest, Issue: 7587 Volume: 10
daemon@ATHENA.MIT.EDU (Perl-Users Digest)
Tue Dec 28 18:10:39 2004
Date: Tue, 28 Dec 2004 15:10:17 -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: 7587
Today's topics:
Re: Is zero even or odd? <a.newmane.remove@eastcoastcz.com>
Re: Is zero even or odd? <krw@att.bizzzz>
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? <dseaman@no.such.host>
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? <krw@att.bizzzz>
Re: Is zero even or odd? <dseaman@no.such.host>
Re: Is zero even or odd? <matternc@comcast.net>
Re: Is zero even or odd? <namdiesttocs@mindspring.com>
Re: Is zero even or odd? <jmw@jmwa.demon.contraspam.yuk>
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? <dseaman@no.such.host>
Re: Is zero even or odd? <hadrainc@earthlink.net>
Re: Is zero even or odd? <george@briar.demon.co.uk>
Re: Is zero even or odd? <george@briar.demon.co.uk>
Re: Is zero even or odd? <george@briar.demon.co.uk>
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? <hadrainc@earthlink.net>
Re: Is zero even or odd? <hadrainc@earthlink.net>
Re: Line continuation in Perl <abigail@abigail.nl>
Re: Perl CGI script using Win::ODBC module - failed log <matthew.garrish@sympatico.ca>
Re: Perl Developer neded. <dha@panix.com>
Re: problems with Perl RegEx match <abigail@abigail.nl>
Re: problems with Perl RegEx match <wyzelli@yahoo.com>
Digest Administrivia (Last modified: 6 Apr 01) (Perl-Users-Digest Admin)
----------------------------------------------------------------------
Date: Tue, 28 Dec 2004 11:15:07 -0800
From: "Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com>
Subject: Re: Is zero even or odd?
Message-Id: <33dpluF3uai9aU1@individual.net>
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.
------------------------------
Date: Tue, 28 Dec 2004 14:15:14 -0500
From: Keith Williams <krw@att.bizzzz>
Subject: Re: Is zero even or odd?
Message-Id: <MPG.1c3b7acfc498f8d9989802@news.individual.net>
In article <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>,
dseaman@no.such.host says...
> On Tue, 28 Dec 2004 11:31:17 -0500, Keith Williams wrote:
> > In article <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>,
> > dseaman@no.such.host says...
> >> >>
> >> >>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
> >> >>
> >> >>No, it isn't. That limit does not exist.
> >>
> >> > Most certainly does. It's zero.
> >>
> >> Wrong. That limit cannot exist because 0^x is undefined for all x < 0.
>
> > "lim x->0 0^x "
>
> > Where is X < 0 in the above?
>
> Look up the definition of limit. Notice that "limit" in the reals means
> "two-sided limit." In particular, that means the left-hand and
> right-hand limits must both exist, and must agree.
Ah, so the lim x->oo 1/x is?
--
Keith
------------------------------
Date: Tue, 28 Dec 2004 19:27:01 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqsc25$n3t$2@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 11:15:07 -0800, Alfred Z. Newmane wrote:
> Dave Seaman wrote:
> But correct me if I'm wrong, isn't returning 1 from 0^0 /mathematically/
> incorrect? I have always known that to be out of the valid domain for
> n^0.
I take it you haven't been reading the thread, since I have given several
mathematical arguments and provided references to support the conclusion
that 0^0 = 1.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 19:34:34 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqscga$n3t$3@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 18:13:29 +0000, John Woodgate wrote:
> I read in sci.electronics.design that Dave Seaman <dseaman@no.such.host>
> wrote (in <cqs5mn$j1c$2@mailhub227.itcs.purdue.edu>) about 'Is zero even
> or odd?', on Tue, 28 Dec 2004:
>>Then you don't know the definition of limit.
> You just want to win the argument, come what may. It is very clear from
> my post that I invoked the right-hand limit. You didn't event attempt to
> deal with my proposition but accused me of ignorance of a concept that I
> did not use in my proposition.
Here's what you snipped:
> In this case, the nature of negative powers of 0 does not affect the
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> limit, as x tends to 0 from positive values, of x^0. Now, are there any
^^^^^
> grounds for supposing (or even proving) that the limit, as x tends to 0
> from positive values, of 0^x differs from the above limit value?
The underlined phrase is simply wrong. You didn't say that "the nature
of negative powers [...] does not affect the *right-hand* limit". You
clearly said that it does not affect the *limit*. So you are lying about
what you said and you are attempting to cover up the lie.
> I will not discuss with you any more.
Good.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 19:45:27 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqsd4n$n3t$4@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 10:29:36 -0800, Alfred Z. Newmane wrote:
> John Woodgate wrote:
>> I read in sci.electronics.design that Alfred Z. Newmane
>> <a.newmane.remov e@eastcoastcz.com> wrote (in
>> <33dkokF3vfnfcU1@individual.net>) about 'Is zero even or odd?', on
>> Tue, 28 Dec 2004:
>>> I've checked every calc I could find with a power function to verify
>>> this. Any graphing type calc yeilds some sort of DOMAIN error, and
>>> any sci calc I've tried simply gives a generic error.
>>
>> Could it be that we are discussing pure mathematics, not calculators,
>> or Ohm's Law, or the price of imaginary apples?
> I was using to prove a point of pure mathematics, that 0^0 is undefined
> (out of the valid domain.)
No, you were using calculators to prove a point about (some) calculators.
I countered with a list of different calculators and programming languages that
give a different result. None of this proves anything about pure mathematics.
But, speaking of pure mathematics:
According to set theory, 0^0 is the cardinality of the set of mappings
from the empty set to itself, which is 1.
Reference: Suppes, _Axiomatic Set Theory_.
Algebraically, let M be a monoid with identity e. Then x^0 = e for each
x in M. The indicated expression is an empty product.
Reference: Lang, _Algebra_.
<http://db.uwaterloo.ca/~alopez-o/math-faq/node40.html#SECTION00530000000000000000>
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 20:18:41 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqsf31$opr$1@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 14:15:14 -0500, Keith Williams wrote:
> In article <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>,
> dseaman@no.such.host says...
>> On Tue, 28 Dec 2004 11:31:17 -0500, Keith Williams wrote:
>> > In article <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>,
>> > dseaman@no.such.host says...
>> >> >>
>> >> >>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
>> >> >>
>> >> >>No, it isn't. That limit does not exist.
>> >>
>> >> > Most certainly does. It's zero.
>> >>
>> >> Wrong. That limit cannot exist because 0^x is undefined for all x < 0.
>>
>> > "lim x->0 0^x "
>>
>> > Where is X < 0 in the above?
>>
>> Look up the definition of limit. Notice that "limit" in the reals means
>> "two-sided limit." In particular, that means the left-hand and
>> right-hand limits must both exist, and must agree.
> Ah, so the lim x->oo 1/x is?
Doesn't exist, because the one-sided limits don't agree.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 20:27:47 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqsfk3$opr$2@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 19:34:34 +0000 (UTC), Dave Seaman wrote:
> On Tue, 28 Dec 2004 18:13:29 +0000, John Woodgate wrote:
>> I read in sci.electronics.design that Dave Seaman <dseaman@no.such.host>
>> wrote (in <cqs5mn$j1c$2@mailhub227.itcs.purdue.edu>) about 'Is zero even
>> or odd?', on Tue, 28 Dec 2004:
>>>Then you don't know the definition of limit.
>> You just want to win the argument, come what may. It is very clear from
>> my post that I invoked the right-hand limit. You didn't event attempt to
>> deal with my proposition but accused me of ignorance of a concept that I
>> did not use in my proposition.
> Here's what you snipped:
>> In this case, the nature of negative powers of 0 does not affect the
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>> limit, as x tends to 0 from positive values, of x^0. Now, are there any
> ^^^^^
>> grounds for supposing (or even proving) that the limit, as x tends to 0
>> from positive values, of 0^x differs from the above limit value?
> The underlined phrase is simply wrong. You didn't say that "the nature
> of negative powers [...] does not affect the *right-hand* limit". You
> clearly said that it does not affect the *limit*. So you are lying about
> what you said and you are attempting to cover up the lie.
I have just noticed that if you remove the comma following "limit" in the
in the underlined passage, it completely changes the meaning. Perhaps
that's what you meant, but I don't understand why. I have repeatedly
explained the difference between two-sided and one-sided limits in this
thread, and the value of the (two-sided) limit is the only point on which
there has been any disagreement as far as I am aware.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 15:32:56 -0500
From: Keith Williams <krw@att.bizzzz>
Subject: Re: Is zero even or odd?
Message-Id: <MPG.1c3b8d06d6a3a33a989803@news.individual.net>
In article <cqsf31$opr$1@mailhub227.itcs.purdue.edu>,
dseaman@no.such.host says...
> On Tue, 28 Dec 2004 14:15:14 -0500, Keith Williams wrote:
> > In article <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>,
> > dseaman@no.such.host says...
> >> On Tue, 28 Dec 2004 11:31:17 -0500, Keith Williams wrote:
> >> > In article <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>,
> >> > dseaman@no.such.host says...
> >> >> >>
> >> >> >>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
> >> >> >>
> >> >> >>No, it isn't. That limit does not exist.
> >> >>
> >> >> > Most certainly does. It's zero.
> >> >>
> >> >> Wrong. That limit cannot exist because 0^x is undefined for all x < 0.
> >>
> >> > "lim x->0 0^x "
> >>
> >> > Where is X < 0 in the above?
> >>
> >> Look up the definition of limit. Notice that "limit" in the reals means
> >> "two-sided limit." In particular, that means the left-hand and
> >> right-hand limits must both exist, and must agree.
>
> > Ah, so the lim x->oo 1/x is?
>
> Doesn't exist, because the one-sided limits don't agree.
Well, that wipes out all the math I ever learned. I guess all that calc
I took in college was for naught.
Lemme guess... You're a math type posting from sci.math.
--
Keith
------------------------------
Date: Tue, 28 Dec 2004 20:59:47 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqshg3$q87$1@mailhub227.itcs.purdue.edu>
On Tue, 28 Dec 2004 15:32:56 -0500, Keith Williams wrote:
> In article <cqsf31$opr$1@mailhub227.itcs.purdue.edu>,
> dseaman@no.such.host says...
>> On Tue, 28 Dec 2004 14:15:14 -0500, Keith Williams wrote:
>> > In article <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>,
>> > dseaman@no.such.host says...
>> >> On Tue, 28 Dec 2004 11:31:17 -0500, Keith Williams wrote:
>> >> > In article <cqs0gk$gpp$1@mailhub227.itcs.purdue.edu>,
>> >> > dseaman@no.such.host says...
>> >> >> >>
>> >> >> >>> Well, 0^0 is a mess. But lim x->0 0^x is well defined.
>> >> >> >>
>> >> >> >>No, it isn't. That limit does not exist.
>> >> >>
>> >> >> > Most certainly does. It's zero.
>> >> >>
>> >> >> Wrong. That limit cannot exist because 0^x is undefined for all x < 0.
>> >>
>> >> > "lim x->0 0^x "
>> >>
>> >> > Where is X < 0 in the above?
>> >>
>> >> Look up the definition of limit. Notice that "limit" in the reals means
>> >> "two-sided limit." In particular, that means the left-hand and
>> >> right-hand limits must both exist, and must agree.
>>
>> > Ah, so the lim x->oo 1/x is?
>>
>> Doesn't exist, because the one-sided limits don't agree.
> Well, that wipes out all the math I ever learned. I guess all that calc
> I took in college was for naught.
Did those calc courses teach you that there is a +infinity and a
-infinity?
> Lemme guess... You're a math type posting from sci.math.
Correct. And I used to teach calculus around 30 years ago.
But there is a way to say the limit exists. You have to work with the
one-point compactification of the reals instead of the two-point
compactification that is commonly taught in calculus courses. That means
you have just a single infinity, instead of a +infinity and a -infinity.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Tue, 28 Dec 2004 16:03:06 -0500
From: Chris Mattern <matternc@comcast.net>
Subject: Re: Is zero even or odd?
Message-Id: <nsmdnUkJfs-RV0zcRVn-hg@comcast.com>
Keith Williams wrote:
> In article <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>,
> dseaman@no.such.host says...
>>
>> Look up the definition of limit. Notice that "limit" in the reals means
>> "two-sided limit." In particular, that means the left-hand and
>> right-hand limits must both exist, and must agree.
>
> Ah, so the lim x->oo 1/x is?
>
Limits as the variable goes to infinity have a different definition
from limits as the variable goes to a finite number, you know.
Just to bore the hell of the newsgroups, I'll give them.
lim x->a f(x) = L means that for any positive number e there exists
a positive number d such that if x is in the interval (a-d, a+d),
except at a itself, then f(x) is in the interval (L-e, L+e).
lim x->oo f(x) = L means that for any positive number e there exists
a positive number M such that if x > M, then f(x) is in the interval
(L-e, L+e).
--
Christopher Mattern
"Which one you figure tracked us?"
"The ugly one, sir."
"...Could you be more specific?"
------------------------------
Date: 28 Dec 2004 21:07:46 GMT
From: Scott Seidman <namdiesttocs@mindspring.com>
Subject: Re: Is zero even or odd?
Message-Id: <Xns95CDA413AC8E0scottseidmanmindspri@130.133.1.4>
Dave Seaman <dseaman@no.such.host> wrote in news:cqshg3$q87$1
@mailhub227.itcs.purdue.edu:
>>> > Ah, so the lim x->oo 1/x is?
>>>
>>> Doesn't exist, because the one-sided limits don't agree.
>
>> Well, that wipes out all the math I ever learned. I guess all that calc
>> I took in college was for naught.
>
> Did those calc courses teach you that there is a +infinity and a
> -infinity?
>
But wouldn't "both sides" of the limit as x -> infinity be referring to
infinity+ and infinity-? This is rather different from saying the limit as
x goes to minus infinity is not the same as the limit as x approaches plus
infinity-- the latter does not refer to both sides of the limit
Scott
------------------------------
Date: Tue, 28 Dec 2004 21:23:49 +0000
From: John Woodgate <jmw@jmwa.demon.contraspam.yuk>
Subject: Re: Is zero even or odd?
Message-Id: <KfYnxdHl7c0BFw+7@jmwa.demon.co.uk>
I read in sci.electronics.design that Dave Seaman <dseaman@no.such.host>
wrote (in <cqsfk3$opr$2@mailhub227.itcs.purdue.edu>) about 'Is zero even
or odd?', on Tue, 28 Dec 2004:
>On Tue, 28 Dec 2004 19:34:34 +0000 (UTC), Dave Seaman wrote:
>> On Tue, 28 Dec 2004 18:13:29 +0000, John Woodgate wrote:
>>> I read in sci.electronics.design that Dave Seaman <dseaman@no.such.host>
>>> wrote (in <cqs5mn$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.
>
>> Here's what you snipped:
>
>>> 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?
>
>> The underlined phrase is simply wrong. You didn't say that "the nature
>> of negative powers [...] does not affect the *right-hand* limit". You
>> clearly said that it does not affect the *limit*. So you are lying about
>> what you said and you are attempting to cover up the lie.
>
>I have just noticed that if you remove the comma following "limit" in the
>in the underlined passage, it completely changes the meaning. Perhaps
>that's what you meant, but I don't understand why. I have repeatedly
>explained the difference between two-sided and one-sided limits in this
>thread, and the value of the (two-sided) limit is the only point on which
>there has been any disagreement as far as I am aware.
>
>
>
Since you have now suggested an interpretation issue, I will respond. I
do not wish to enter a discussion on commas, but the phrase 'as x tends
to 0 from positive values' is indeed intended to qualify the preceding
word 'limit'.
But for me that is not the issue. I do not LIE on newsgroups - there is
no point - but I do make mistakes; everyone does. I suggest that your
accusation of 'lying' was, and is, unjustified, whether my post was
correct or not correct.
--
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 21:45:50 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <mvk3t0pmmashjbdhk09n5f643mdpdfb00h@4ax.com>
On Tue, 28 Dec 2004 09:44:55 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:
>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.
>
Check back when you are awake.
------------------------------
Date: Tue, 28 Dec 2004 21:48:23 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <82l3t09lankat59p02h2vqu9c4f4gcimlf@4ax.com>
On Tue, 28 Dec 2004 11:05:22 -0600, John Fields
<jfields@austininstruments.com> wrote:
>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
Sorry Johnny if you are going to indulge in abstractions, you have to
observe the rules.
------------------------------
Date: Tue, 28 Dec 2004 21:50:45 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <o7l3t0pk5icdf3m0f46q9v0fdh4tsnsete@4ax.com>
On Tue, 28 Dec 2004 09:46:05 -0600, russotto@grace.speakeasy.net
(Matthew Russotto) wrote:
>>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.
No you can't go that route either.
------------------------------
Date: Tue, 28 Dec 2004 21:58:18 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqsktq$rld$1@mailhub227.itcs.purdue.edu>
On 28 Dec 2004 21:07:46 GMT, Scott Seidman wrote:
> Dave Seaman <dseaman@no.such.host> wrote in news:cqshg3$q87$1
> @mailhub227.itcs.purdue.edu:
>>>> > Ah, so the lim x->oo 1/x is?
>>>>
>>>> Doesn't exist, because the one-sided limits don't agree.
>>
>>> Well, that wipes out all the math I ever learned. I guess all that calc
>>> I took in college was for naught.
>>
>> Did those calc courses teach you that there is a +infinity and a
>> -infinity?
>>
> But wouldn't "both sides" of the limit as x -> infinity be referring to
> infinity+ and infinity-? This is rather different from saying the limit as
> x goes to minus infinity is not the same as the limit as x approaches plus
> infinity-- the latter does not refer to both sides of the limit
Oh, sorry. For some reason I read "lim x->oo" as "lim x->0", probably
because we were supposed to be talking about the relation between
two-sided and one-sided limits, and that concept doesn't apply at all for
limits at infinity. What I was saying was (assuming the two-point
compactification):
lim_{x->0+} 1/x = +infinity
lim_{x->0-} 1/x = -infinity
lim_{x->} 1/x does not exist because the one-sided limits don't agree.
On the other hand, we have
lim_{x->+oo} 1/x = 0,
lim_{x->-oo} 1/x = 0,
but there is no such thing as a two-sided limit there, unless we are
dealing with the one-point compactification of the reals, in which case
lim_{x->oo} 1/x = 0,
but we normally don't speak of one-sided limits in that scenario.
--
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 22:00:15 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <0dl3t0phevuvrl8t5qd79jre1vvio985vh@4ax.com>
On Tue, 28 Dec 2004 16:09:56 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> 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.
Chuckle, except for the fact that 0^0 is meaningless undefined babble.
n^0 = 1 where n is a positive number, not equal to 0.
------------------------------
Date: Tue, 28 Dec 2004 22:04:23 -0000
From: "George Dishman" <george@briar.demon.co.uk>
Subject: Re: Is zero even or odd?
Message-Id: <cqsl78$4o9$1@news.freedom2surf.net>
"vonroach" <hadrainc@earthlink.net> wrote in message
news: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.
Not really, simply cooling a resistive material
won't usually reduce the resistance to zero. The
superconducting state is fundamentally different.
George
------------------------------
Date: Tue, 28 Dec 2004 22:13:54 -0000
From: "George Dishman" <george@briar.demon.co.uk>
Subject: Re: Is zero even or odd?
Message-Id: <cqslp3$4ub$1@news.freedom2surf.net>
"John Fields" <jfields@austininstruments.com> wrote in message
news:ms91t0dhjdf80j8l804mo2ic098gv2ndil@4ax.com...
> On Mon, 27 Dec 2004 23:26:19 -0000, "George Dishman"
> <george@briar.demon.co.uk> wrote:
>>
>>Ok. In that you argue that, if you set the
>>voltage and current numerically equal, then
>>since the ratio is 1 for all values, it
>>implies that it remains 1 for a numerical
>>value of 0. His counter argument is that
>>the choice of setting the values to be equal
>>is arbitrary and it is just as valid to set
>>the voltage to be, say, double that of the
>>current hence by the same argument, 0/0=2.
>>
>>Since one can choose any ratio before taking
>>the limit as both approach zero, the same
>>argument can prove 0/0 to be equal to any
>>arbitrary value, hence falsifying the claim
>>that 0/0 has one and only one value.
>>
>>To refute his counter-argument and prove your
>>claim that the value of 1 is unique, you need
>>to provide a reason why the statement 0/0=2
>>(or any value other than 1) cannot be true.
>
> ---
> 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.
So far you are assuming the result you are
trying to prove, that the ratio of numerator
and denominator is to be 1.
> 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.
I like that however while the statement 0=0
is obviously true, it isn't exhaustive. We
also have
0 = k * 0
hence by your method
0/0 = limit as x->0 of (k*x)/x
hence
0/0 = k for all constant k
You still fail to prove the claim of
uniqueness for the value of 1.
George
------------------------------
Date: Tue, 28 Dec 2004 22:16:07 -0000
From: "George Dishman" <george@briar.demon.co.uk>
Subject: Re: Is zero even or odd?
Message-Id: <cqslt7$52v$1@news.freedom2surf.net>
"vonroach" <hadrainc@earthlink.net> wrote in message
news:82l3t09lankat59p02h2vqu9c4f4gcimlf@4ax.com...
> On Tue, 28 Dec 2004 11:05:22 -0600, John Fields
> <jfields@austininstruments.com> wrote:
>
>>How comforting it must be for you to know that somewhere, on a dusty
>>old bookrack, lies a little book which releases you from the drudgery
>>of thinking.
>>
>
>>John Fields
> Sorry Johnny if you are going to indulge in abstractions, you have to
> observe the rules.
The task at hand is to show whether the rule
is valid or otherwise. Can you do that?
George
------------------------------
Date: Tue, 28 Dec 2004 22:17:14 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <p4m3t05s5p9u5m2utl50pmj89csf1vhs0c@4ax.com>
On Tue, 28 Dec 2004 15:32:56 -0500, Keith Williams <krw@att.bizzzz>
wrote:
>In article <cqsf31$opr$1@mailhub227.itcs.purdue.edu>,
>dseaman@no.such.host says...
>> On Tue, 28 Dec 2004 14:15:14 -0500, Keith Williams wrote:
>> > In article <cqs4v5$j1c$1@mailhub227.itcs.purdue.edu>,
>> > dseaman@no.such.host says...
>> >> On Tue, 28 Dec 2004 11:31:17 -0500, Keith Williams wrote:
>> >> > In article <cqs0gk$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.
>>
>> > Ah, so the lim x->oo 1/x is?
>>
>> Doesn't exist, because the one-sided limits don't agree.
>
>Well, that wipes out all the math I ever learned. I guess all that calc
>I took in college was for naught.
>
>Lemme guess... You're a math type posting from sci.math.
No, he's making it up as he goes along. The limit called for is a very
small number greater than 1/0 which is meaningless and undefined.
What problem called for this math abstraction? There is a practical
limit on how small `things' can get - beyond that limit,, one is just
blowing smoke through one's butthole. These are the uncertainties that
we live with.
------------------------------
Date: Tue, 28 Dec 2004 22:35:07 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <grm3t05vn4g0i5ktfp24sdjn9tjojoafcu@4ax.com>
On Tue, 28 Dec 2004 20:59:47 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> wrote:
>Correct. And I used to teach calculus around 30 years ago.
>
>But there is a way to say the limit exists. You have to work with the
>one-point compactification of the reals instead of the two-point
>compactification that is commonly taught in calculus courses. That means
>you have just a single infinity, instead of a +infinity and a -infinity.
Even when I studied 55 years ago, we knew that there were an infinity
of infinities. Have you ever seen a euclidean graph of a tangent?
Each `infinity' has to be defined. They come in very large to
infinitesimal . They can be finite (surface of a sphere) or infinite.
I prefer a moderate finite infinity with whipped cream and a cherry. I
can envision any continuum yielding many infinities. But quantization
makes the concept poison. Doesn't the statement that a quantity
_approaches_ infinity, imply that it is never reached?
------------------------------
Date: Tue, 28 Dec 2004 22:42:57 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <2sn3t09b0ocp2q4ava30s97qei3v0522n7@4ax.com>
On 28 Dec 2004 21:07:46 GMT, Scott Seidman
<namdiesttocs@mindspring.com> wrote:
>Dave Seaman <dseaman@no.such.host> wrote in news:cqshg3$q87$1
>@mailhub227.itcs.purdue.edu:
>
>>>> > Ah, so the lim x->oo 1/x is?
>>>>
>>>> Doesn't exist, because the one-sided limits don't agree.
>>
>>> Well, that wipes out all the math I ever learned. I guess all that calc
>>> I took in college was for naught.
>>
>> Did those calc courses teach you that there is a +infinity and a
>> -infinity?
>>
>
>But wouldn't "both sides" of the limit as x -> infinity be referring to
>infinity+ and infinity-? This is rather different from saying the limit as
>x goes to minus infinity is not the same as the limit as x approaches plus
>infinity-- the latter does not refer to both sides of the limit
>
>Scott
Both sides of what? x _approaches_ infinity, it never gets there. If 0
exists then some functions _approach_ + infinity or approach -
infinity. Infinity is very elusive. It like the ultimate structure of
matter/energy is never seen or measured with certainty.
------------------------------
Date: Tue, 28 Dec 2004 23:01:17 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <04p3t0p61hftmfgo60c8sfsq5h2k68gau3@4ax.com>
On Tue, 28 Dec 2004 09:51:12 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:
>2^0 = 1
>1^0 = 1
>0^0 = ERROR, DOMAIN (hence the limit)
>(-1)^0 = 1
>(-2)^0 = 1
(-1^1/2)^0 =?
or ( i )^0 =?
------------------------------
Date: Tue, 28 Dec 2004 23:03:29 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <mfp3t0hmlbik696qtpkrv1a5lteikscvhf@4ax.com>
On Tue, 28 Dec 2004 18:14:54 +0000, John Woodgate
<jmw@jmwa.demon.contraspam.yuk> wrote:
>Could it be that we are discussing pure mathematics, not calculators, or
>Ohm's Law, or the price of imaginary apples?
>--
It was never made clear whether the `apple' in question was a fruit
or a computer.
------------------------------
Date: Tue, 28 Dec 2004 23:04:33 GMT
From: vonroach <hadrainc@earthlink.net>
Subject: Re: Is zero even or odd?
Message-Id: <fjp3t01rnu2cqlv7cmq2hvh2l4libfggi1@4ax.com>
On Tue, 28 Dec 2004 10:29:36 -0800, "Alfred Z. Newmane"
<a.newmane.remove@eastcoastcz.com> wrote:
>I was using to prove a point of pure mathematics, that 0^0 is undefined
>(out of the valid domain.)
Didn't you know that?
------------------------------
Date: 28 Dec 2004 20:29:45 GMT
From: Abigail <abigail@abigail.nl>
Subject: Re: Line continuation in Perl
Message-Id: <slrnct3ghp.non.abigail@alexandra.abigail.nl>
Michele Dondi (bik.mido@tiscalinet.it) wrote on MMMMCXXXVII September
MCMXCIII in <URL:news:qt03t0hbghr08mcnf46q64a3al21ahmqlv@4ax.com>:
\\ On 24 Dec 2004 08:04:24 GMT, Abigail <abigail@abigail.nl> wrote:
\\
\\ >"Somebody" is correct, in Perl1 to Perl5, you can put whitespace between
\\ >tokens. Including newlines. (Perl6 will be different, putting whitespace
\\ >between certain tokens will change the meaning of your program. Or be
\\ >a syntax error. Fun, fun, fun!)
\\
\\ Indeed will be slightly less free-form than we're used to (in some
\\ senses). I know that you're particularly upset by this choice, in fact
\\ I seem to remeber you even wrote something like "Perl6 will pass
\\ Python on the wrong side"; OTOH I think we all have something about
\\ Perl6 that we just can't feel at ease with, but aren't your concerns
\\ just a little bit exaggerated? I mean: yes, you won't be allowed e.g.
\\ to leave whitespace after a sigil or brackets, but you will still be
\\ allowed to do this provided you explicitly put the dereferencer there,
\\ which incidentally happens to be a simple dot.
No, I'm not exaggerating. I'm talking about a change that will effect
almost *EVERY* line of code I write. And many lines will be effected
multiple times.
I've been able to put whitespace between a function/aggregate and
the parenthesis/brackets in every language I remember programming
in in the past 20+ years.
And the problem is, in many cases, putting whitespace there isn't
even a compile error. It just quietly changes the meaning of your
program.
In Perl6:
$var1 = cos (0) * 2; # Equals 1.
$var2 = cos(0) * 2; # Equals 2.
Abigail
--
use lib sub {($\) = split /\./ => pop; print $"};
eval "use Just" || eval "use another" || eval "use Perl" || eval "use Hacker";
------------------------------
Date: Tue, 28 Dec 2004 15:04:24 -0500
From: "Matt Garrish" <matthew.garrish@sympatico.ca>
Subject: Re: Perl CGI script using Win::ODBC module - failed login on
Message-Id: <9%iAd.19276$nV.584664@news20.bellglobal.com>
"brandony" <byoukstetter@hotmail.com> wrote in message
news:1104250796.965780.120670@z14g2000cwz.googlegroups.com...
>
> Matt Garrish wrote:
>
>> If I understand you correctly, it sounds like you haven't specified
> the
>> username and password for the DSN properly in the ODBC manager (i.e.,
> there
>> is no default user and password for that DSN). Go to Settings --
> Control
>> Panel -- Admin Tools -- ODBC Settings (or something similar depending
> on
>> your version of Windows) and trying testing the connection. If you
> can't
>> connect, then go over the settings and see what you've missed. Also,
> make
>> sure that you've set it up as a System DSN and not a User DSN.
>>
>> It definitely doesn't sound like a Perl problem, though. I would
> personally
>> recommend you switch to the DBI and DBD::ODBC modules, however, as
> support
>> for Win32::ODBC is suspect.
>>
> I don't think its a problem with the ODBC connection. It is a System
> DSN and I always get the green light when testing the connnection at
> the end of setup. Any other ideas? I will look at the DBD::ODBC
> modules. BTW, I agree that this doesnt seem like a perl problem, but
> rather a setup issue with respect to the web site context (user rights
> is was my first inclination). I just thought someone here may have had
> similar issues.
>
A lot depends on what type of database you're trying to connect to. MySQL
allows you to store the username and password for the DSN, but others like
MS SQL require login information to be supplied when you establish the
connection. The only thing I can suggest is that you try a newsgroup that
deals with your particular database. The problem itself is language agnostic
and ODBC specific, as you'd run into the same problem connecting to the
database regardless of which language you're using (which is why you're
getting a system error and not a perl error).
Matt
------------------------------
Date: Tue, 28 Dec 2004 19:24:00 +0000 (UTC)
From: "David H. Adler" <dha@panix.com>
Subject: Re: Perl Developer neded.
Message-Id: <slrnct3cmg.a1i.dha@panix2.panix.com>
On 2004-12-27, Chad Columbus <ccolumbu@hotmail.com> wrote:
> I am pretty sure I should not be posting this here
Give that person a kewpie doll!
Longstanding Usenet tradition dictates that such postings go into
groups with names that contain "jobs", like "misc.jobs.offered", not
technical discussion groups like the ones to which you posted.
Had you read and understood the Usenet user manual posted frequently to
"news.announce.newusers", you might have already known this. :) (If
n.a.n is quieter than it should be, the relevent FAQs are available at
http://www.faqs.org/faqs/by-newsgroup/news/news.announce.newusers.html)
Another good source of information on how Usenet functions is
news.newusers.questions (information from which is also available at
http://www.geocities.com/nnqweb/).
Please do not explain your posting by saying "but I saw other job
postings here". Just because one person jumps off a bridge, doesn't
mean everyone does. Those postings are also in error, and I've
probably already notified them as well.
If you have questions about this policy, take it up with the news
administrators in the newsgroup news.admin.misc.
http://jobs.perl.org may be of more use to you
Yours for a better usenet,
dha
--
David H. Adler - <dha@panix.com> - http://www.panix.com/~dha/
I believe myself to be the daughter of a one-eyed space robot named
Malcolm. -Fallon Young, http://www.bobbins.org/d/20000915.html
------------------------------
Date: 28 Dec 2004 20:39:19 GMT
From: Abigail <abigail@abigail.nl>
Subject: Re: problems with Perl RegEx match
Message-Id: <slrnct3h3n.non.abigail@alexandra.abigail.nl>
mitch (mitch_christow@biogen.com) wrote on MMMMCXXXVII September MCMXCIII
in <URL:news:1104248521.746602.313050@f14g2000cwb.googlegroups.com>:
%%
%% In terms of indenting, my code is beautifully indented, however while
%% posting it, the tabs and spaces had been removed. Next time I'll add
%% some HTML code to the posting, just so that it gets formatted properly.
Adding HTML code is a sure way of getting killfiled by those who are
most likely to answer your queries.
If whitespace gets removed, get a better newsagent.
Abigail
--
perl -Mstrict='}); print "Just another Perl Hacker"; ({' -le1
------------------------------
Date: Tue, 28 Dec 2004 22:31:20 GMT
From: "Peter Wyzl" <wyzelli@yahoo.com>
Subject: Re: problems with Perl RegEx match
Message-Id: <Y8lAd.92197$K7.52540@news-server.bigpond.net.au>
"mitch" <mitch_christow@biogen.com> wrote in message
news:1104248521.746602.313050@f14g2000cwb.googlegroups.com...
: Hi everyone,
:
: Thanks first of all for all the great comments and suggestions. So
: Abigail, you were right, I foolishly forgot to close a silly brace.
: That should teach me to write code after only sleeping for two hours
: (boy do I feel sheepish).
:
: In terms of indenting, my code is beautifully indented, however while
: posting it, the tabs and spaces had been removed. Next time I'll add
: some HTML code to the posting, just so that it gets formatted properly.
Don't do that. Just replace the tabs with an appropriate number of spaces
(3 or 4 should be fine)
--
Wyzelli
------------------------------
Date: 6 Apr 2001 21:33:47 GMT (Last modified)
From: Perl-Users-Request@ruby.oce.orst.edu (Perl-Users-Digest Admin)
Subject: Digest Administrivia (Last modified: 6 Apr 01)
Message-Id: <null>
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------------------------------
End of Perl-Users Digest V10 Issue 7587
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