Is zero even or odd?

[Alfred Z. Newmane]

vonroach wrote:

On Mon, 20 Dec 2004 15:21:14 -0800, "Alfred Z. Newmane"
a.newmane.remove@eastcoastcz.com> wrote:

Except for the fact that: 0 / 0 = undefined

Or actually more correct: n / 0 = undefined

Really, Al Z? Where did you get that doctorate in math? Various
middle eastern types have worked hard to see that was not the case.

Did you have a refutal somewhere?

 

[robert j. kolker]

Alfred Z. Newmane wrote:

Then why can you not perform 1/0 ? (or n/0)

If n/0 for n not 0 had a value then it would be equal to 0 and not equal
to 0 at the same time. Contradictions are not permitted.

Bob Kolker

 

[John Larkin]

On Tue, 21 Dec 2004 20:36:30 +0000, Nick Atty
<nospam@nandj.freeserve.co.uk> wrote:

And let's not, please, have the endless(!) debate about whether infinity
means anything to computers, whether C is a turing complete language
etc.

Please.

I got tired of worrying about math exceptions in embedded systems so
wrote a fixed-point math package that always produces legal answers
and never crashes. The basic variable format is a 64-bit thing, 32.32
bits (32 bit signed integer plus 32 bits of fraction) which handles
most practical realtime values pretty well. The biggest possible
positive and negative values are defined to be "infinity", and
anything that computes bigger is just clamped there.


0 / anything = 0

nonzero/0 = infinity (sign maintained, of course)

small / big = 0

big * big = infinity

sqrt(negative) = 0


and stuff like that.


John

 

[Alfred Z. Newmane]

robert j. kolker wrote:

Alfred Z. Newmane wrote:


Then why can you not perform 1/0 ? (or n/0)

If n/0 for n not 0 had a value then it would be equal to 0 and not
equal to 0 at the same time. Contradictions are not permitted.

I know, that was my silent point (that ultimately, you cannot div by
zero.)

 

[Alfred Z. Newmane]

Nicholas O. Lindan wrote:

"robert j. kolker" <nowhere@nowhere.net> wrote

Then why can you not perform 1/0 ? (or n/0)

If n/0 for n not 0 had a value then it would be equal to 0 and not
equal to 0 at the same time.

???

The common contrarian take is:

1 / 0 = oo
n / 0 = n * oo
0 / 0 = 0 * oo = 1

oo (infinity isn't a number) so you cannot use it this way.

 

[vonroach]

On Wed, 22 Dec 2004 12:07:32 -0500, Shawn Corey
<shawn.corey@sympatico.ca> wrote:

vonroach wrote:
Then infinity is undefined?

I did not write this. Please be more careful.
Infinity is a mathematical concept like all mathematics. Cantor has
most complete exploration to date in my opinion.
Mathematics in general are human inventions that serve two purposes to
count and to concisely illustrate scientific concepts.

 

[John W. Kennedy]

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.
--
John W. Kennedy
"The pathetic hope that the White House will turn a Caligula into a
Marcus Aurelius is as naďve as the fear that ultimate power inevitably
corrupts."
-- James D. Barber (1930-2004).

 

[Torkel Franzen]

"John W. Kennedy" <jwkenne@attglobal.net> writes:

Aleph-1 is at least aleph-null^aleph-null.

On what do you base this assertion?

 

[Michael Mendelsohn]

"Nicholas O. Lindan" schrieb:

0/0 pops up now and then: The system does the right thing if
this is treated as 1.

If in measuring a resistor, we find 0.0A at 0.0V, is the resistance 1
Ohm, then?

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

 

[Michael Mendelsohn]

"Nicholas O. Lindan" schrieb:

"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?

Touche.

But, yes, I'll say it is 1, just not in conventional ohms.
At 0.0A and 0.0V any scaling factor can apply to the volts
and amps without changing the measurement:

1 new volt / 1 new amp = new value of the resistor.

0 new volts / 0 new amps = 1 * (1 volt / 1 amp) = new value of the resistor.

Value of the resistor = 1 new ohm.

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.

Hence, vacuum/an insulator/air has a resistance of 1 new Ohm?

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

 

[Dave Seaman]

On Thu, 23 Dec 2004 19:02:20 GMT, 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.

No, not at all. It's not a function in the ordinary sense, but a
generalized function. It's a linear functional defined on a certain
function space.

<http://mathworld.wolfram.com/DeltaFunction.html>.

Clearly the infinities are
failures of the theory,

Or a failure of the mathematics.

Definitely not.



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

 

[robert j. kolker]

Dave Seaman wrote:

No, not at all. It's not a function in the ordinary sense, but a
generalized function. It's a linear functional defined on a certain
function space.

Here is an analogy. A function is like a vector. A delta "function" is
like a one form.

Bob Kolker

 

[vonroach]

On Thu, 23 Dec 2004 19:48:08 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

I'm lost.

Then you have come to the right door! Come in and join the others.

 

[vonroach]

On Thu, 23 Dec 2004 20:18:14 +0000, John Woodgate
<jmw@jmwa.demon.contraspam.yuk> wrote:

Although it's called aleph-one, no-one knows whether it is
the *next* infinity after aleph-null, or whether there are other
infinities in between.

I know, but I'm not about to share that information with nitwits who
post here.

 

[vonroach]

On Thu, 23 Dec 2004 22:00:35 +0000 (UTC), George Cox
<george_coxanti@spambtinternet.com.invalid> wrote:

the question is, is 2^{aleph_0} the next infinity after aleph_0? (And
generally, is 2^{aleph_{alpha}} the next infinity after aleph_{alpha}?)

No, to be or not to be is the question.

 

[vonroach]

On Fri, 24 Dec 2004 08:21:39 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

The latter part of the paragraph seems to support the view that
c = continuum = cardinality of the reals = aleph-0 ^ aleph-0 = aleph^1
which you claim in the first two sentences to be false.

Dazed and confused again.

That is the usual outcome when one follows the abstract creations of
the mind such as mathematics too far. A sip of reality may sober you
again.

 

[vonroach]

On Thu, 23 Dec 2004 19:18:24 +0100, 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?

Er...how many resistances have you really measured? Did you read the
instructions carefully?

 

[vonroach]

On Thu, 23 Dec 2004 19:56:18 GMT, "Nicholas O. Lindan" <see@sig.com>
wrote:

Value of the resistor = 1 new ohm.

Illustration of the ability of the abstract brain to cope with
foolishness.

 

[Fred Bloggs]

vonroach wrote:

On 20 Dec 2004 07:02:45 -0800, merlyn@stonehenge.com (Randal L.
Schwartz) wrote:


This is a troll. *Negative*? Can I have some of the drug you're
smoking?


That's no good Randy, no matter how much you buy, you still have
nothing. Coincidentally with constant use the measurable IQ approaches
zero as a limit.

For once I agree with you- several living examples extant here.

 

[Torkel Franzen]

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?