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Is zero even or odd?

F

Franz Heymann

Jan 1, 1970
0
Tam/WB2TT said:
The two are not the same.

The definition of the ratio a/b is

a/b = r iff b*r = a

for the case of n/0 there is no r such that r*0 = n (follows from the
definition of zero. Therefore n/0 (for non zero n) *does not exist*.

On the other hand, for 0/0, every r qualifies since for every r, r*0 =
0 (the definition of zero, again). Therefore, 0/0 is truly undefined,
in the sense that it is impossible to *uniquely* assign a value to the
ratio r.

Mati Meron | "When you argue with a fool,
[email protected] | chances are he is doing just
the same"

It depends on how you get there, [sin(x)]/x is certainly defined for all
values of x including 0 and infinity.

If you knew any maths worth talking about, you would have known that
sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
The first is undefined and the second is unity.

Now it is your turn: What do you know about sin (infinity) / infinity
?

Franz
 
F

Franz Heymann

Jan 1, 1970
0
Steven Lord said:
Nicholas O. Lindan said:
David Kastrup said:
0/0 is clearly, if anything, a constant expression. And it turns out
[to some] that its value is undefined.

Better minds than can be found here have argued this and not reached
any conclusion. 'Undefined' is the answer given by the teacher in the
7th grade, and will serve for all practical purposes.

Maybe what is needed is a New Number = '*' (or something) = Any
Number You
Want.

Just FYI, if you're performing arithmetic using the IEEE 754
standard,

I doubt if there are any mathematicians who care a hoot about
definitions made by engineers for computational convenience

[snip]

Franz
 
Franz Heymann said:
Steven Lord said:
Nicholas O. Lindan said:
0/0 is clearly, if anything, a constant expression. And it turns out
[to some] that its value is undefined.

Better minds than can be found here have argued this and not reached
any conclusion. 'Undefined' is the answer given by the teacher in the
7th grade, and will serve for all practical purposes.

Maybe what is needed is a New Number = '*' (or something) = Any
Number You
Want.

Just FYI, if you're performing arithmetic using the IEEE 754
standard,

I doubt if there are any mathematicians who care a hoot about
definitions made by engineers for computational convenience

[snip]

Well, then, how about y'all stop crossposting from Hell to breakfast?

Followups set.

Xho
 
The two are not the same.

The definition of the ratio a/b is

a/b = r iff b*r = a

for the case of n/0 there is no r such that r*0 = n (follows from the
definition of zero. Therefore n/0 (for non zero n) *does not exist*.

On the other hand, for 0/0, every r qualifies since for every r, r*0 =
0 (the definition of zero, again). Therefore, 0/0 is truly undefined,
in the sense that it is impossible to *uniquely* assign a value to the
ratio r.

Mati Meron | "When you argue with a fool,
[email protected] | chances are he is doing just the same"

It depends on how you get there, [sin(x)]/x is certainly defined for all
values of x including 0 and infinity.
That's a different thing. Here you're talking not about a plain value
but a limit (of an infinite set of values). And this depends how you
get there. Thus, [sin(0)]/0 is undefined. On the other hand,
lim_x->0 {[sin[x]/x} is defined and equal to 1.

Mati Meron | "When you argue with a fool,
[email protected] | chances are he is doing just the same"
 
M

Michael Mendelsohn

Jan 1, 1970
0
Nicholas O. Lindan said:
Oh, this sounds like even more fun. Something we know even less
about ...

I would say about a black-hole's-worth.

Well, if there's at least one universe inside a black hole, then that
universe could contain another black hole, and so forth.
Because of the Schwarzschild radius, the is at least one universe inside
the black hole separate from ours.
By induction, the answer is: infinitely many.

Cheers
Michael
 
T

Tam/WB2TT

Jan 1, 1970
0
Franz Heymann said:
Tam/WB2TT said:
0 can't be divided by itself,

Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1

It works if the only three numbers in the universe are
0, 1, and infinity -- A number system that seems very
suited to usenet.

Except for the fact that: 0 / 0 = undefined

Or actually more correct: n / 0 = undefined

The two are not the same.

The definition of the ratio a/b is

a/b = r iff b*r = a

for the case of n/0 there is no r such that r*0 = n (follows from the
definition of zero. Therefore n/0 (for non zero n) *does not exist*.

On the other hand, for 0/0, every r qualifies since for every r, r*0 =
0 (the definition of zero, again). Therefore, 0/0 is truly undefined,
in the sense that it is impossible to *uniquely* assign a value to the
ratio r.

Mati Meron | "When you argue with a fool,
[email protected] | chances are he is doing just
the same"

It depends on how you get there, [sin(x)]/x is certainly defined for all
values of x including 0 and infinity.

If you knew any maths worth talking about, you would have known that
sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
The first is undefined and the second is unity.
Tell that to all the book publishers who print curves for sinx/x.
Now it is your turn: What do you know about sin (infinity) / infinity
?

Franz
No problem. Sin x is bounded between +/- 1 for all values of x. A finite
number divided by infinity is 0.

Tam
 
W

Willem

Jan 1, 1970
0
) ) <snip>
)> If you knew any maths worth talking about, you would have known that
)> sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
)> The first is undefined and the second is unity.

Tam/WB2TT wrote:

) Tell that to all the book publishers who print curves for sinx/x.

If you zoom in on those printed curves far enough, you'll notice that
there is no ink at the actual point (0,1).


SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT
 
N

Nicholas O. Lindan

Jan 1, 1970
0
Richards Noah (IFR LIT MET) said:
Wrong- where do you get off saying (2*0)/0= 2*(0/0) ?

The Dorsh Road stop on the #9 line. But thank you for your
kind and thoughtful response. You maybe got off a few stops
earlier?

If I treat 0 as an imaginary number, which is what it may
be - what with the way imaginations go wild over the subject,
then 0 <> (2 * 0), as are sqrt(-1) <> 2*sqrt(-1) and
oo <> 2 * oo.

On adding to infinity there is much controversy, some claim

1 + oo <> oo + 1

This gets multiple infinities out of some paradox but is
too bizarre even for me.

There is also a school of thought:

oo < n * oo

Some reject multiplication and claim the next infinity worth
talking about is:

oo = n + oo = n * oo < oo^oo

Infinity, like 0, seems to be imaginary. Nobody can produce
-nothing-, as nobody can produce -everything-.

But to claim:

n / 0 is illegal and Sister Prudence will rap your knuckles if
you think otherwise.

Well, how petit bourgeois can one get?

Angels and pin-heads anyone? At least Sister Pru would approve.

* * *

Slightly OT, is there an accepted ASCII-gram for square root?

And shouldn't someone add a travel cruise group to the distribution.
 
N

Nicholas O. Lindan

Jan 1, 1970
0
Franz Heymann said:
If you knew any maths worth talking about,

I guess in your book I don't, but I won't let that stop me.
you would have known that
sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.

Gee, and all that analysis I have been doing using sinc(x) as a
test impulse is all wrong: the function is discontinuous and not
differentiable or integrable. Zeno Rules!

I imagine then that lim(x->2) <> 2. Makes about much sense to me,
but then I think (2 * 0)/(3 * 0) = 2/3,
 
N

Nicholas O. Lindan

Jan 1, 1970
0
Well, then, how about y'all stop crossposting from Hell to breakfast?

We are being inclusive. We just got lectured that inclusiveness is a
universal _good thing_, so we are trying it out.
 
N

Nicholas O. Lindan

Jan 1, 1970
0
Mati Meron said:
"When you argue with a fool, chances are he is doing just the same"

I nominate this as the summation of the debate.
 
M

Matthew Russotto

Jan 1, 1970
0
I guess in your book I don't, but I won't let that stop me.


Gee, and all that analysis I have been doing using sinc(x) as a
test impulse is all wrong: the function is discontinuous and not
differentiable or integrable. Zeno Rules!

sinc(x) is a useful function that's defined as sin(pi*x)/pi*x when x
is not equal to 0 and as 1 when x is equal to zero. But
sin (pi*x)/pi*x is discontinous at zero.
 
J

John Woodgate

Jan 1, 1970
0
I read in sci.electronics.design that Nicholas O. Lindan <[email protected]>
Slightly OT, is there an accepted ASCII-gram for square root?

I've seen v/(x) used; it's fairly evident what it means. I just found
that decimal 175 is an 'overscore' character, ¯, which means that v/¯(x)
could be used.

How about) for cube root?
 
J

John Woodgate

Jan 1, 1970
0
I read in sci.electronics.design that Matthew Russotto
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'.
 
J

John Woodgate

Jan 1, 1970
0
I read in sci.electronics.design that John Woodgate <[email protected]
How about) for cube root?

My newsreader jibbed at that, as you can see, so yours may have, too. It
had the exponent-3 character, decimal 179, before the v/¯(x) group.
 
E

Ed Murphy

Jan 1, 1970
0
Slightly OT,

Only slightly?
is there an accepted ASCII-gram for square root?

_______
_ /(x+y)*z
v2 would be my suggestion, or / ------- for more complex expressions.
v a+2

sqrt(2) or 2^.5 is generally more manageable, though.
And shouldn't someone add a travel cruise group to the distribution.

*scratches head* *googles* Ah, there's a cruise line named Infinity.
 
M

Michael Mendelsohn

Jan 1, 1970
0
John said:
I've seen v/(x) used; it's fairly evident what it means. I just found
that decimal 175 is an 'overscore' character, ¯, which means that v/¯(x)
could be used.

I suggest

²v¯(a+b) = v¯(a+b) = (a+b)^(1/2) = (a+b)^½ = sqrt(a+b)

³v¯(a+b) = (a+b)^(1/3)

The ASCII-grams have the worst readability of the bunch, IMO.

Cheers
Michael
 
D

David Kastrup

Jan 1, 1970
0
Willem said:
) ) <snip>
)> If you knew any maths worth talking about, you would have known that
)> sin(0) / 0 is not the same as the limit of sin(x) / x as x tends to 0.
)> The first is undefined and the second is unity.

Tam/WB2TT wrote:

) Tell that to all the book publishers who print curves for sinx/x.

If you zoom in on those printed curves far enough, you'll notice
that there is no ink at the actual point (0,1).

Exactly at 0 (and nowhere else), there is a vertical smear from
roadkill. If you ever wondered where Schrödinger's cat ended up after
all, this is it.
 
D

David Kastrup

Jan 1, 1970
0
Ed Murphy said:
Only slightly?


_______
_ /(x+y)*z
v2 would be my suggestion, or / ------- for more complex expressions.
v a+2

sqrt(2) or 2^.5 is generally more manageable, though.

Well Emacs Calc suggests

___________
| (x + y) z
| ---------
\| a + 2

and there is something to be said for your Usenet reader to be able to
manipulate simple formulas graphically.
 
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