# Is zero even or odd?

Discussion in 'Electronic Design' started by Gactimus, Dec 20, 2004.

1. ### Franz HeymannGuest

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

2. ### Franz HeymannGuest

standard,

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

[snip]

Franz

3. ### Guest

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

Followups set.

Xho

4. ### Guest

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,
| chances are he is doing just the same"

5. ### Michael MendelsohnGuest

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

6. ### Tam/WB2TTGuest

Tell that to all the book publishers who print curves for sinx/x.
No problem. Sin x is bounded between +/- 1 for all values of x. A finite
number divided by infinity is 0.

Tam

7. ### WillemGuest

) ) <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

8. ### Nicholas O. LindanGuest

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

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.

9. ### Nicholas O. LindanGuest

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!

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

10. ### Nicholas O. LindanGuest

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

11. ### Nicholas O. LindanGuest

I nominate this as the summation of the debate.

12. ### Matthew RussottoGuest

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.

13. ### John WoodgateGuest

I read in sci.electronics.design that Nicholas O. Lindan <>
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.

14. ### John WoodgateGuest

I read in sci.electronics.design that Matthew Russotto
Is it? Does the limit of its differential differ as x->0+ and as x->0-?
If not, it's 'squeezed'.

15. ### John WoodgateGuest

I read in sci.electronics.design that John Woodgate <
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.

16. ### Ed MurphyGuest

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.

Yes it is!

Michele

18. ### Michael MendelsohnGuest

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

19. ### David KastrupGuest

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.

20. ### David KastrupGuest

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.