[25326] in Perl-Users-Digest
Perl-Users Digest, Issue: 7571 Volume: 10
daemon@ATHENA.MIT.EDU (Perl-Users Digest)
Fri Dec 24 21:10:32 2004
Date: Fri, 24 Dec 2004 18:10:09 -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 Fri, 24 Dec 2004 Volume: 10 Number: 7571
Today's topics:
Re: Is zero even or odd? <eorgemw@covad.net>
Re: Is zero even or odd? <see@sig.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? <torkel@sm.luth.se>
Re: Is zero even or odd? <nospam@nospam.com>
Re: Is zero even or odd? <nospam@nospam.com>
Re: Is zero even or odd? <invalid@msgid.michael.mendelsohn.de>
Re: Is zero even or odd? (Matthew Russotto)
Re: Is zero even or odd? <invalid@msgid.michael.mendelsohn.de>
Re: Is zero even or odd? <dseaman@no.such.host>
Re: Is zero even or odd? (Matthew Russotto)
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? <jmw@jmwa.demon.contraspam.yuk>
Re: Is zero even or odd? (Matthew Russotto)
Perl and pm path question. <tmwilspamnot@png.com>
Digest Administrivia (Last modified: 6 Apr 01) (Perl-Users-Digest Admin)
----------------------------------------------------------------------
Date: Fri, 24 Dec 2004 11:39:02 -0800
From: George Weinberg <eorgemw@covad.net>
Subject: Re: Is zero even or odd?
Message-Id: <jsros0ln5nicaq3b6bis5k4si7lnkchtkf@4ax.com>
On Thu, 23 Dec 2004 19:54:20 +0000, Dirk Bruere at Neopax
<dirk@neopax.com> wrote:
>Kevin Aylward wrote:
>
>> Dirk Bruere at Neopax wrote:
>>
>>>Gordon Weast wrote:
>>>
>>>
>>>>Another is renormalization theory in QED (Quantum Electrodynamics).
>>>>There are several infinities in the theory that appeared to make
>>>>the results nonsense. However, if you keep track very carefully,
>>>>you can get the infinities to cancel and come up with predictions
>>>>that match measurements very accurately.
>>>
>>>And physicists think it an ugly bodge.
>>
>>
>> Actually, I think the physicists think its just a bit annoying, its the
>> mathematicians that think its the ugly bodge.
>>
>>
>>>Clearly the infinities are
>>>failures of the theory,
>>
>>
>> Or a failure of the mathematics.
>
>Is there a difference?
Actually, there is, maybe. At least some people believe that it should
be possible to make the procedure mathematically rigorous, so the
question is, whose job is that? In my opinion, a mathematician should
have to do the work, but after he does it, we'll call him a physicist!
George
------------------------------
Date: Fri, 24 Dec 2004 19:46:25 GMT
From: "Nicholas O. Lindan" <see@sig.com>
Subject: Re: Is zero even or odd?
Message-Id: <lm_yd.12220$Z47.2572@newsread2.news.atl.earthlink.net>
"Alfred Z. Newmane" <a.newmane.remove@eastcoastcz.com>
> What's this zero supposed to represent? The "zero" root? Isn't that
> dividing by zero?
> n^0 = 1; zeroroot(n) = undefined
Oh, it gets worse.
Conventional disallows 1 / 0
Unconventional allows 1 / 0 and sets it to oo
Expression Conventional Unconventional
reduced value reduced value Comment
1 / 0 verboten oo
0^2 0 0 * 0 - is (0 * 0) < or > 0 ?
0^1 0 0
0^0 ? ? - is it 0 or is it 1 in either system?
0 - 0 0 ? - or irreducible or disallowed
0 - 0 - 0 0 ??
0 - (0 - 0) 0 ???
0^0 is a mess in either system.
Aside from 0^0, the conventional system wins in the question mark
race.
Is there a solution to 0 - 0?
Does allowing division by 0 disallow 0 - 0.
Lucky Christmas is upon us. This is definitely something that can
not be understood unless one is drunk....
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
------------------------------
Date: Fri, 24 Dec 2004 20:06:21 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqhsrt$8bs$1@mailhub227.itcs.purdue.edu>
On Fri, 24 Dec 2004 18:17:17 GMT, Nicholas O. Lindan wrote:
> "Dave Seaman" <dseaman@no.such.host> wrote
>> Perhaps I should have said that the Continuum Hypothesis (CH) is the
>> "hypothesis" (rather than the "proposition") that c = aleph_1. The final
>> clause says that CH is neither provable nor disprovable; that's what
>> "independent of the axioms" means.
> Agreed, figured out what I thought you meant, and I think that is what
> you thought you meant.
> In the original it was hard to tell assertions from negations from
> perambulations. It seemed to negate an assertion then assert the first
> assertion and conclude that nothing could be asserted or negated.
> Did I get that right?
I know what I said, but I don't see how I can answer questions about how
it seemed to you. Such propositions are independent of my axioms.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Fri, 24 Dec 2004 20:30:51 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqhu9r$8bs$2@mailhub227.itcs.purdue.edu>
On Fri, 24 Dec 2004 15:22:55 GMT, Fred Bloggs wrote:
> Torkel Franzen wrote:
>> Fred Bloggs <nospam@nospam.com> writes:
>>
>>
>>>... because the non-existence of infinity strictly between countability
>>>and first uncountability ( power set of countability) has been shown to
>>>be equivalent to the Axiom of Choice.
>>
>>
>> You're mistaken about this. Why these ill-informed exchanges in all
>> these unrelated groups?
>>
> Are you saying this has not been established yet?
You made so many mistakes in that one sentence that it's hard to know
where to begin.
For one thing, the nonexistence of cardinals strictly between aleph_0 and
aleph_1 is a matter of definition. Without the axiom of choice, the
possibility exists that there may be cardinals that are not comparable
with either of those, but there still can't be any that are strictly
between. In other words, aleph_1 is certainly minimal among the
uncountable cardinals, even without AC.
For another thing, the power set of the naturals has the same cardinality
as the reals, namely 2^aleph_0 = c, the cardinality of the continuum.
The assertion that c = aleph_1 is called the Continuum Hypothesis (CH).
Not only has it not been established "yet"; it's been established that CH
will never be proved or disproved in ZFC (Zermelo-Frankel set theory plus
the axiom of choice).
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: 24 Dec 2004 21:59:56 +0100
From: Torkel Franzen <torkel@sm.luth.se>
Subject: Re: Is zero even or odd?
Message-Id: <vcbekhf5s4z.fsf@beta19.sm.ltu.se>
Dave Seaman <dseaman@no.such.host> writes:
> ...but it's fairly
> easy to see that ZF + GCH -> AC, since ZF + GCH implies that every
> cardinal is an aleph,
"Fairly easy" seems to me an exaggeration. Sierpinski's proof is far
from trivial.
------------------------------
Date: Fri, 24 Dec 2004 21:36:20 GMT
From: Fred Bloggs <nospam@nospam.com>
Subject: Re: Is zero even or odd?
Message-Id: <41CC8B74.2090701@nospam.com>
Dave Seaman wrote:
> On Fri, 24 Dec 2004 15:22:55 GMT, Fred Bloggs wrote:
>
>
>
>>Torkel Franzen wrote:
>>
>>>Fred Bloggs <nospam@nospam.com> writes:
>>>
>>>
>>>
>>>>... because the non-existence of infinity strictly between countability
>>>>and first uncountability ( power set of countability) has been shown to
>>>>be equivalent to the Axiom of Choice.
>>>
>>>
>>> You're mistaken about this. Why these ill-informed exchanges in all
>>>these unrelated groups?
>>>
>>
>
>
>>Are you saying this has not been established yet?
>
>
> You made so many mistakes in that one sentence that it's hard to know
> where to begin.
>
> For one thing, the nonexistence of cardinals strictly between aleph_0 and
> aleph_1 is a matter of definition. Without the axiom of choice, the
> possibility exists that there may be cardinals that are not comparable
> with either of those, but there still can't be any that are strictly
> between. In other words, aleph_1 is certainly minimal among the
> uncountable cardinals, even without AC.
As you said aleph_1 is minimal by definition, and without AC it may not
be a bound of all the uncountable infinities- there may be an infinity
of aleph_1's- the ordering is not total. Interesting that you say AC->
the ordering of the cardinals will be total.
>
> For another thing, the power set of the naturals has the same cardinality
> as the reals, namely 2^aleph_0 = c, the cardinality of the continuum.
> The assertion that c = aleph_1 is called the Continuum Hypothesis (CH).
I think Cantor's original statement was that there is no infinity
strictly intermediate to countability and c- which of course means
c=alepha_1 if it exists.
> Not only has it not been established "yet"; it's been established that CH
> will never be proved or disproved in ZFC (Zermelo-Frankel set theory plus
> the axiom of choice).
Right- it is undecidable- that much has been proved in ZFC- the CH is
independent of AC. Supposedly H. Woodin has constructed a plausible
axiom recently which if incorporated into ZFC implies the CH is false.
Nonetheless, it makes no sense to speak of anything as being "true" as
either system is self-consistent, the assumption of CH or /CH will never
lead to a contradiction of the axioms.
------------------------------
Date: Fri, 24 Dec 2004 21:44:37 GMT
From: Fred Bloggs <nospam@nospam.com>
Subject: Re: Is zero even or odd?
Message-Id: <41CC8D71.3090406@nospam.com>
Dave Seaman wrote:
> On Fri, 24 Dec 2004 16:44:34 GMT, Fred Bloggs wrote:
>
>
>>Wouldn't that contradict Cohen? I see that ZF + GCH-> CH, and now you
>>say ZF + GCH -> Axiom of Choice, when Cohen showed /CH + ZFC leads to no
>>contradiction. Certainly /CH-> /GCH under ZFC.
>
>
>
> And then? I don't see where you are going with this, but it's fairly
> easy to see that ZF + GCH -> AC, since ZF + GCH implies that every
> cardinal is an aleph, which is a roundabout way of saying that every set
> can be well ordered.
I don't think you mean well-ordered in the algebraic sense- you mean a
total ordering on the cardinals.
------------------------------
Date: Sat, 25 Dec 2004 00:23:49 +0100
From: Michael Mendelsohn <invalid@msgid.michael.mendelsohn.de>
Subject: Re: Is zero even or odd?
Message-Id: <41CCA505.672836DC@msgid.michael.mendelsohn.de>
John Fields schrieb:
> On Fri, 24 Dec 2004 00:17:14 +0100, Michael Mendelsohn
> >John Fields schrieb:
> >> On Thu, 23 Dec 2004 22:45:26 +0100, Michael Mendelsohn
> >> >> "Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote
> >> >> > If in measuring a resistor, we find 0.0A at 0.0V, is the resistance 1
> >> >> > Ohm, then?
> >
> >> >When checking it turned out that some thief had actually stolen the
> >> >resistor where 0V,0A was measured. The circuit was broken, but noone
> >> >noticed because the voltage was zero.
> >
> >> In truth, the E in
> >>
> >> E
> >> R = ---
> >> I
> >>
> >> refers to the voltage _across_ the resistor, (a shunt, was it?) which
> >> you didn't measure. What you measured was the voltage from the low
> >> side of where the resistor was supposed to be to ground, which gave
> >> you zero volts which corresponded, also, to zero amps. Had you
> >> measured the voltage _across_ where the resistor was supposed to be
> >
> >Well, I did - do you think I'm stupid? ;)
>
> ---
> Not so far ;)
Thanks!
> ---
>
> >The problem is, the measurement was automatic, and since there was
> >short-circuit somewhere (presumably in parallel to the supposed
> >resistor), the voltage was zero across the measurement points even
> >before the resistor was stolen. The current is of course measured the
> >proper way.
>
> ---
> I'm not trying to be insulting, but would you mind explaining how the
> current was measured?
By putting an instrument into the circuit where I wanted to measure the
current.
Presumbly that branch of the circuit had a box marked "resistor" in it,
which should have contained a 100 Ohm resistor, so measured as if that
had been there, but when I opened the box, I found it empty.
We're talking about hypothetical boxes and hypothetical resistors here,
because I am trying to model a 0/0 quotient using an electrical circuit
in the attempt show to Nicholas O. Lindan ("Nick" for short) that simply
assuming that this quotient is 1 is a little reckless.
> ---
>
> >The software computed resistance by Nick's rules and hence never noticed
> >anything unusual.
>
> ---
> Nick's rules?
See above: 0/0=1
> I'm in the dark about that. Clue me in?
Well, that's because the light doesn't work. I think someone stole ... -
but you already know that. ;)
> ---
>
> >> you would have measured the entire supply voltage minus what was being
> >> dropped across the load by the current flowing through the meter and
> >> you would have concluded that by subtracting the meter current that
> >> you would have had:
> >>
> >> E E
> >> R = --- = --- = oo
> >> I 0
> >>
> >> Which would have been right!
> >
> >Unless E=0 too, in which case the result is 1 (says Nick).
> >
> >On a short circuit you can detect no voltage, but you can measure a
> >current.
> >
> > E 0
> > R = --- = --- = 0
> > I I
> >
> >This leads to a contradiction when E=I=0.
>
> ---
> So it would seem, but a short across the resistor would still have
> resulted in a voltage drop across the resistor equal to the parallel
> resistance of the resistor and the short multiplied by the current
> through that parallel resistance. Since there's no such thing as a
> perfect short and the resistance of the resistor was known beforehand,
If the short is "short enough", it can be perfect enough for my
instrument to not detect the voltage drop.
> the "short" and the anomalous current (which you said you measured)
> through it should have pointed to either the resistor failing shorted,
> an external short developing across the resistor, or some dirty
> bastard stealing the resistor and putting a short across where it was,
> no?
The short is not in the path of the current I've measured. I've only
invented the short to explain why there can be 0V across the (stolen?)
resistor.
+---------------------(V)----+
| |
(-)-----o-------[__R__]---o---(A)----o--------(+)
|____________________________|
the short
>
> How much was that resistor worth, anyway?
A lot of thought.
Cheers
Michael
--
Still an attentive ear he lent Her speech hath caused this pain
But could not fathom what she meant Easier I count it to explain
She was not deep, nor eloquent. The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
------------------------------
Date: Fri, 24 Dec 2004 17:32:07 -0600
From: russotto@grace.speakeasy.net (Matthew Russotto)
Subject: Re: Is zero even or odd?
Message-Id: <2r6dnUgS2f5qO1HcRVn-tw@speakeasy.net>
In article <cfDyd.12532$ue4.3369@fe12.lga>,
John W. Kennedy <jwkenne@attglobal.net> wrote:
>Nicholas O. Lindan wrote:
>> But the size of the set of real numbers is Aleph 1 (oo^2).
>
>Aleph-1 is at least aleph-null^aleph-null.
But isn't c = 2^aleph-null, and aleph-1 is possibly less than c?
------------------------------
Date: Sat, 25 Dec 2004 00:35:14 +0100
From: Michael Mendelsohn <invalid@msgid.michael.mendelsohn.de>
Subject: Re: Is zero even or odd?
Message-Id: <41CCA7B2.EBC8E205@msgid.michael.mendelsohn.de>
"Nicholas O. Lindan" schrieb:
> "Michael Mendelsohn" <invalid@msgid.michael.mendelsohn.de> wrote
> > When checking it turned out that some thief had actually stolen the
> > resistor where 0V,0A was measured. The circuit was broken, but noone
> > noticed because the voltage was zero.
>
> The circuit wasn't connected. Therefore no measurement was being
> made. V = IR has no relevance. R < oo to close the circuit and
> for the equation to apply.
I notice that you're refusing to treat the R = OV/OA quotient like any
other quotient, saying the outcome is "no measurement". In fact, you'd
probably be saying that for any measurement with I=0A since you'd argue
the circuit isn't connected.
But when a mathematician told you that the mathematics "isn't connected"
for n/0, you refused to accept that, even though (to me) the
circumstances are quite identical.
I am hoping that you would take a step back, slap your forehead and say
"Oh, why didn't I see that before?", but it may not happen.
In either case, I wish you happy holidays!
Michael
--
Still an attentive ear he lent Her speech hath caused this pain
But could not fathom what she meant Easier I count it to explain
She was not deep, nor eloquent. The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls
------------------------------
Date: Fri, 24 Dec 2004 23:31:15 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqi8s3$esa$1@mailhub227.itcs.purdue.edu>
On 24 Dec 2004 21:59:56 +0100, Torkel Franzen wrote:
> Dave Seaman <dseaman@no.such.host> writes:
>> ...but it's fairly
>> easy to see that ZF + GCH -> AC, since ZF + GCH implies that every
>> cardinal is an aleph,
> "Fairly easy" seems to me an exaggeration. Sierpinski's proof is far
> from trivial.
Yes, in fact, I cancelled that article after thinking about it a bit more.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Fri, 24 Dec 2004 17:44:49 -0600
From: russotto@grace.speakeasy.net (Matthew Russotto)
Subject: Re: Is zero even or odd?
Message-Id: <pt6dnanCFIJsNFHcRVn-1g@speakeasy.net>
In article <tYieQTBX$6yBFwru@jmwa.demon.co.uk>,
John Woodgate <noone@yuk.yuk> wrote:
>I read in sci.electronics.design that Matthew Russotto
><russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
>hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
>>John Woodgate <noone@yuk.yuk> wrote:
>>>I read in sci.electronics.design that Matthew Russotto
>>><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>>>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>>>But sin (pi*x)/pi*x is
>>>>discontinous at zero.
>>>
>>>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>>>If not, it's 'squeezed'.
>>
>>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>>
>Squeezed: if the limits are equal, the value of the function at the
>limit point cannot differ from the limit value.
Certainly not a valid theorem.
------------------------------
Date: Fri, 24 Dec 2004 23:47:15 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqi9q2$esa$3@mailhub227.itcs.purdue.edu>
On Fri, 24 Dec 2004 21:44:37 GMT, Fred Bloggs wrote:
> Dave Seaman wrote:
>> On Fri, 24 Dec 2004 16:44:34 GMT, Fred Bloggs wrote:
>>
>>
>>>Wouldn't that contradict Cohen? I see that ZF + GCH-> CH, and now you
>>>say ZF + GCH -> Axiom of Choice, when Cohen showed /CH + ZFC leads to no
>>>contradiction. Certainly /CH-> /GCH under ZFC.
>>
>>
>>
>> And then? I don't see where you are going with this, but it's fairly
>> easy to see that ZF + GCH -> AC, since ZF + GCH implies that every
>> cardinal is an aleph, which is a roundabout way of saying that every set
>> can be well ordered.
> I don't think you mean well-ordered in the algebraic sense- you mean a
> total ordering on the cardinals.
As I mentioned elsewhere, I actually cancelled that article shortly after
posting it. But yes, I did mean that GCH -> every set can be
well-ordered, though the proof of that is not as simple as I implied.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Fri, 24 Dec 2004 23:43:27 +0000 (UTC)
From: Dave Seaman <dseaman@no.such.host>
Subject: Re: Is zero even or odd?
Message-Id: <cqi9iu$esa$2@mailhub227.itcs.purdue.edu>
On Fri, 24 Dec 2004 21:36:20 GMT, Fred Bloggs wrote:
> Dave Seaman wrote:
>> On Fri, 24 Dec 2004 15:22:55 GMT, Fred Bloggs wrote:
>>>Torkel Franzen wrote:
>>>>Fred Bloggs <nospam@nospam.com> writes:
>>>>>... because the non-existence of infinity strictly between countability
>>>>>and first uncountability ( power set of countability) has been shown to
>>>>>be equivalent to the Axiom of Choice.
>>>> You're mistaken about this. Why these ill-informed exchanges in all
>>>>these unrelated groups?
>>>Are you saying this has not been established yet?
>> You made so many mistakes in that one sentence that it's hard to know
>> where to begin.
>> For one thing, the nonexistence of cardinals strictly between aleph_0 and
>> aleph_1 is a matter of definition. Without the axiom of choice, the
>> possibility exists that there may be cardinals that are not comparable
>> with either of those, but there still can't be any that are strictly
>> between. In other words, aleph_1 is certainly minimal among the
>> uncountable cardinals, even without AC.
> As you said aleph_1 is minimal by definition, and without AC it may not
> be a bound of all the uncountable infinities- there may be an infinity
> of aleph_1's- the ordering is not total. Interesting that you say AC->
> the ordering of the cardinals will be total.
The ordinals are totally ordered, and AC -> every cardinal can be
bijectively mapped to some ordinal. The standard definition with AC is
that a cardinal is an initial ordinal, meaning an ordinal that cannot be
bijectively mapped to any of its members.
>> For another thing, the power set of the naturals has the same cardinality
>> as the reals, namely 2^aleph_0 = c, the cardinality of the continuum.
>> The assertion that c = aleph_1 is called the Continuum Hypothesis (CH).
> I think Cantor's original statement was that there is no infinity
> strictly intermediate to countability and c- which of course means
> c=alepha_1 if it exists.
If what exists? Certainly c and aleph_1 both exist in ZF.
>> Not only has it not been established "yet"; it's been established that CH
>> will never be proved or disproved in ZFC (Zermelo-Frankel set theory plus
>> the axiom of choice).
> Right- it is undecidable- that much has been proved in ZFC- the CH is
> independent of AC. Supposedly H. Woodin has constructed a plausible
> axiom recently which if incorporated into ZFC implies the CH is false.
> Nonetheless, it makes no sense to speak of anything as being "true" as
> either system is self-consistent, the assumption of CH or /CH will never
> lead to a contradiction of the axioms.
I did not say anything was "true." You are merely confirming what I
said.
--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
------------------------------
Date: Sat, 25 Dec 2004 00:38:15 +0000
From: John Woodgate <jmw@jmwa.demon.contraspam.yuk>
Subject: Re: Is zero even or odd?
Message-Id: <bpLDMRA3ZLzBFw3L@jmwa.demon.co.uk>
I read in sci.electronics.design that Matthew Russotto
<russotto@grace.speakeasy.net> wrote (in <pt6dnanCFIJsNFHcRVn-
1g@speakeasy.net>) about 'Is zero even or odd?', on Fri, 24 Dec 2004:
>In article <tYieQTBX$6yBFwru@jmwa.demon.co.uk>,
>John Woodgate <noone@yuk.yuk> wrote:
>>I read in sci.electronics.design that Matthew Russotto
>><russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
>>hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>>In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
>>>John Woodgate <noone@yuk.yuk> wrote:
>>>>I read in sci.electronics.design that Matthew Russotto
>>>><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>>>>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>>>>But sin (pi*x)/pi*x is
>>>>>discontinous at zero.
>>>>
>>>>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>>>>If not, it's 'squeezed'.
>>>
>>>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>>>
>>Squeezed: if the limits are equal, the value of the function at the
>>limit point cannot differ from the limit value.
>
>Certainly not a valid theorem.
>
Please publish an understandable refutation.
--
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: Fri, 24 Dec 2004 19:39:26 -0600
From: russotto@grace.speakeasy.net (Matthew Russotto)
Subject: Re: Is zero even or odd?
Message-Id: <tuSdnbCk1uRTWVHcRVn-pg@speakeasy.net>
In article <bpLDMRA3ZLzBFw3L@jmwa.demon.co.uk>,
John Woodgate <noone@yuk.yuk> wrote:
>I read in sci.electronics.design that Matthew Russotto
><russotto@grace.speakeasy.net> wrote (in <pt6dnanCFIJsNFHcRVn-
>1g@speakeasy.net>) about 'Is zero even or odd?', on Fri, 24 Dec 2004:
>>In article <tYieQTBX$6yBFwru@jmwa.demon.co.uk>,
>>John Woodgate <noone@yuk.yuk> wrote:
>>>I read in sci.electronics.design that Matthew Russotto
>>><russotto@grace.speakeasy.net> wrote (in <EZOdnaqXBOVFPVbcRVn-
>>>hA@speakeasy.net>) about 'Is zero even or odd?', on Thu, 23 Dec 2004:
>>>>In article <It+Hd8BnRPyBFw8A@jmwa.demon.co.uk>,
>>>>John Woodgate <noone@yuk.yuk> wrote:
>>>>>I read in sci.electronics.design that Matthew Russotto
>>>>><russotto@grace.speakeasy.net> wrote (in <RqadnScDqOI5fVXcRVn-
>>>>>jg@speakeasy.net>) about 'Is zero even or odd?', on Tue, 21 Dec 2004:
>>>>>>But sin (pi*x)/pi*x is
>>>>>>discontinous at zero.
>>>>>
>>>>>Is it? Does the limit of its differential differ as x->0+ and as x->0-?
>>>>>If not, it's 'squeezed'.
>>>>
>>>>I'm not sure what you mean by 'squeezed'; it's piecewise continuous.
>>>>
>>>Squeezed: if the limits are equal, the value of the function at the
>>>limit point cannot differ from the limit value.
>>
>>Certainly not a valid theorem.
>>
>Please publish an understandable refutation.
Counterexample:
Consider the function f(x) which is zero at all points except zero, where
it is one. Now consider the limits of f(x) as x approaches zero from
either side.
------------------------------
Date: Fri, 24 Dec 2004 19:56:37 -0500
From: Tom Wiley <tmwilspamnot@png.com>
Subject: Perl and pm path question.
Message-Id: <pan.2004.12.25.00.56.37.498819@png.com>
I am making pretty good progress with learning perl and am trying both
PerlQt and Perl/TK. Tk works fine but PerlQt doesnt.
I think this is more of a straight perl question rather than a problem on
one of the above rads.
Here is the start of a very simple PerlQt tutorial...
#!/usr/bin/perl -w
use strict;
use blib;
use Qt;
(snip)
When I run it I get the following error...
$ ./tutorial1.pl
Cannot find blib even in /home/knoppix/programming/perlqt/../../../../..
BEGIN failed--compilation aborted at ./tutorial1.pl line 4. $
(This seems to be a strange message. It almost seems to say "Hey dummy, I
didn't find blib.pm where it should have been so I looked in the directory
that you started the program from and I didn't find it there either!")
Ok, fair complaint. It can't find a .pm module that I have told it that
is needed.
But... If I look at my @INC it looks like this...
perl -V
(snip)
@INC:
/etc/perl
/usr/local/lib/perl/5.8.4
/usr/local/share/perl/5.8.4
/usr/lib/perl5
/usr/share/perl5
/usr/lib/perl/5.8
/usr/share/perl/5.8
/usr/local/lib/site_perl
And if I do a locate on the alledged missing module I get this...
$ locate blib.pm
/usr/local/lib/perl/5.8.4/blib.pm
/usr/share/perl/5.8.4/blib.pm
So...
blib.pm IS in a path pointed to by @INC. However, no matter where I put
blib.pm it can't be found.
What am I not seeing here? This would seem to be a simple path problem.
Thanks
TW
------------------------------
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>
Administrivia:
#The Perl-Users Digest is a retransmission of the USENET newsgroup
#comp.lang.perl.misc. For subscription or unsubscription requests, send
#the single line:
#
# subscribe perl-users
#or:
# unsubscribe perl-users
#
#to almanac@ruby.oce.orst.edu.
NOTE: due to the current flood of worm email banging on ruby, the smtp
server on ruby has been shut off until further notice.
To submit articles to comp.lang.perl.announce, send your article to
clpa@perl.com.
#To request back copies (available for a week or so), send your request
#to almanac@ruby.oce.orst.edu with the command "send perl-users x.y",
#where x is the volume number and y is the issue number.
#For other requests pertaining to the digest, send mail to
#perl-users-request@ruby.oce.orst.edu. Do not waste your time or mine
#sending perl questions to the -request address, I don't have time to
#answer them even if I did know the answer.
------------------------------
End of Perl-Users Digest V10 Issue 7571
***************************************
