Is zero even or odd?

[Fred Bloggs]

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

Really? You are the arrogant bastard- and I'm not quite sure what you
know 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.

 

[Fred Bloggs]

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.

 

[vonroach]

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
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!

There you go spoiling the fun by really measuring something. But can
resistance ever be infinite? Is it truly 0 even at absolute 0 temp or
there about? Is there no limit on the accuracy of the equipment used
to measure it? I hesitate to add, making the instrument `infinitely'
accurate?

 

[Torkel Franzen]

... 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?

 

[vonroach]

E 0
R = --- = --- = 0
I I

This leads to a contradiction when E=I=0.

Of course. E = MC^2

 

[vonroach]

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.

Sorta like N/0 - irrelevant nonsense.

 

[Dave Seaman]

Ho hum. What isn't a function? We are discussing QED.

Yes, sorry. I read in the wrong context.

 

[Fred Bloggs]

You're mistaken about this. Why these ill-informed exchanges in all
these unrelated groups?

Are you saying this has not been established yet?

 

[vonroach]

1 apple, 2 apples ... but sqrt(-1)apples, why that's only
in your imagination.

I'm afraid so. If you can't see that you are brainwashed . An apple is
an apple is an apple - furthermore each is unique. We dream up
numbers for handling them when 2 or 3 are encountered together. We can
imagine 0 apples and infinite apples - abstractions too. Why did you
think we would have trouble with imaginary or irrational apples?

 

[vonroach]

It can do, but that is not the only reason for sqrt(-1). Its certainly
not how it came about in the first place.

It just pops up in mathematic operations. A little puzzling at first
like pi and phi.

 

[Dave Seaman]

Referencing:

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.

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.

 

[vonroach]

Is there a difference?

That was my question.

 

[Fred Bloggs]

You're mistaken about this. Why these ill-informed exchanges in all
these unrelated groups?

See:

Cohen,P.J., "The Independence of the Continuum Hypothesis." Proc. Nat.
Acad. Sci. U.S.A. 50 1143-148, 1963.

My statement was based on an off hand remark by Halmos in his General
Topology, and he was almost certainly referring to this result, the date
is about right.

 

[Androcles]

I'm afraid so. If you can't see that you are brainwashed . An apple is
an apple is an apple - furthermore each is unique. We dream up
numbers for handling them when 2 or 3 are encountered together. We can
imagine 0 apples and infinite apples - abstractions too. Why did you
think we would have trouble with imaginary or irrational apples?

How far does an apple roll if it makes two turns?
Exact answer in apple diameters, please.
Androcles

 

[Torkel Franzen]

See:

Cohen,P.J., "The Independence of the Continuum Hypothesis." Proc. Nat.
Acad. Sci. U.S.A. 50 1143-148, 1963.

The independence of the continuum hypothesis has no apparent
relation to your statement. Note that the axiom of choice does not
imply the continuum hypothesis. The generalized continuum hypothesis
does imply the axiom of choice.

 

[Alfred Z. Newmane]

I did not write this. Please be more careful.

Yes you did.
See below.

-------------------------------------------------------

From: vonroach <[email protected]>
Newsgroups:
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Subject: Re: Is zero even or odd?
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Date: Wed, 22 Dec 2004 14:49:45 GMT
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You guys are arguing two different things. The argument that 0/0 is the set
of all integers/reals/whatever you are using is the set theory response to
the question. However, the more commonly used form is the algebraicly
accepted argument that states that division is a function of the forms: Z /
Z -> Q, R / R -> R, etc. In this definition, division by 0 is undefined for
all Z or R, including 0. So, you are both correct, but arguing different
things.

Then infinity is undefined?

 

[Alfred Z. Newmane]

Nicholas O. Lindan wrote:
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.

Yes, that's my point. Keep track of oo, don't merge it with
numbers.

j [sqrt(-1)] isn't a number but we still mix it up with numbers.

Of course it is a number, thats why we treat it as such.

Ok what it's value then?
..
..
..
..
Exactly, it has no defined value.

 

[Alfred Z. Newmane]

Nicholas O. Lindan wrote:
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.

Yes, that's my point. Keep track of oo, don't merge it with
numbers.

j [sqrt(-1)] isn't a number but we still mix it up with numbers.

Of course it is a number, thats why we treat it as such.

Ok what it's value then?
.
.
.
.
Exactly, it has no defined value.

(Was refering to infinity (oo))

 

[Alfred Z. Newmane]

Alfred Z. Newmane wrote:

Well, if you move out of pure math into something more applied,
like physics or signal processing, you find a nice little thing
called the Dirac delta function. This seems to have confounded
mathemeticians for a while before they finally came around and
decided that it really does work.

This wonderful function has infinite height and zero width, yet
it has area 1. Granted, you can work with a limit as the width
goes to 0, but you don't have to.

Think Fourier series and Fourier analysis. These wouldn't work
without the Dirac delta function.

A wonderful example of 0 * oo = 1.

Except for the fact it doesn't follow the basic mathematic principal of
0 * n = 0 (anything times zero is zero.) Infinity is undefined. Perhaps
I'm missing something here but how exactly do they get 1 from that?

 

[Alfred Z. Newmane]

Here's an example of how I draw equations in ASCII art.

_
/ theta / psi pi \ / psi pi \
| sin | ----- + --- | + cos | ----- + --- |
| \ 2 4 / \ 2 4 /
| ------------------------------------------------- , d psi
| ____________________________
| / 2 / psi pi \
| / 1 + tan | ----- - --- |
_/ 0 \/ \ 2 4 /

^^^

What's this zero supposed to represent? The "zero" root? Isn't that
dividing by zero?
n^0 = 1; zeroroot(n) = undefined

What it really comes down to is this:

If
sqrt(4) = 2
can be written as
4^(1/2) = 2,
then
zeroroot(n) = undefined
can be written as
n^(1/0) = undefined,
can it not?