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Is zero even or odd?

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

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  1. 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

  2. standard,

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


  3. Guest

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

    Followups set.

  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. 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.

  6. Tam/WB2TT

    Tam/WB2TT Guest

    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.

  7. Willem

    Willem Guest

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

    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.
  9. 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. We are being inclusive. We just got lectured that inclusiveness is a
    universal _good thing_, so we are trying it out.
  11. I nominate this as the summation of the debate.
  12. 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. I read in 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.

    How about) for cube root?
  14. I read in 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. I read in 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 Murphy

    Ed Murphy Guest

    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.
    *scratches head* *googles* Ah, there's a cruise line named Infinity.
  17. Yes it is!

  18. 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.

  19. 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. 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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