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Is zero even or odd?

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

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  1. There is a lot I don't know, but this isn't an example of such.
    No it isn't, it is an operator on all numbers, integer or otherwise.
    Sure, you can have *another* meaning to the / operator in a different
    context, but this aint that context. This discussion is about a/b as
    usually understood in arithmetic.
    My, my, aint you a clever dude...
    Nope. I am using a well understood definition of division as applicable
    to this argument.

    Kevin Aylward
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
  2. Fred Bloggs

    Fred Bloggs Guest

    We were talking about integers, and therefore 0/0={all integers}. You
    want to talk about reals then 0/0={ all reals }. Are you saying that 0*x
    I just told you how it is understood.
    Really? You never have told us what your "well understood" definition
    is- so what exactly are you "using" here?
  3. I read in that Kevin Aylward
    I don't know, but the word 'meaningless' is meaningful. I hope that is
    of no help whatsoever. (;-)
  4. John Fields

    John Fields Guest

  5. John Fields

    John Fields Guest

  6. John Fields

    John Fields Guest


    b = 1
    a = b
    a^2 = ab
    a^2 - b^2 = ab - b^2
    (a+b)(a-b) = b(a-b)
    a+b = b
    1+1 = 1
  7. BB

    BB Guest

    Well sure. 0 /+N is illogical. It's like asking:
    "How many universes are in a black hole ?"
    0/-N makes more sense. Therefore, black holes
    have lots of useless anti-matter inside of them. ;-)
  8. Man, like, we don' need no steenkin' facts ...
  9. 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.
  10. Oh, this sounds like even more fun. Something we know even less
    about ...

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

    But I don't believe in black holes.

    Makes me an expert on the subject ...
  11. BB

    BB Guest

    How about some easier questions:

    How many black holes are there in the universe ?

    Is it meaningful to ask infinity/0 ?

    Are we going to need some kind of mathematics
    where the second question is somewhat meaningful
    in order to answer the first question ?

    Is the last (sic) question meaningful ?
    There are black holes stealing odd socks out of
    my laundry.
  12. 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
  13. Steven Lord

    Steven Lord Guest


    Just FYI, if you're performing arithmetic using the IEEE 754 standard, then
    n/0 for n not equal to 0 is the infinity with the same sign as n (i.e. -1/0
    is -Inf while 1/0 is +Inf). Under the standard, 0/0 is NaN (Not a Number).
    If you scroll down to "Special Operations" on this page:

    you'll see some of the operations on numbers that can be represented in the
    form given by the standard that give "special" results.

    Professor William Kahan also discusses some of these types of operations in
    these lecture notes, starting around page 6:
  14. Ever hear the one about the Grandmother and blowing eggs?

    IEEE passed a standard. Well, heck then, the issue is settled.
    Lets all go home.

  15. An even number plus an even number equals an even number.

    An odd number plus an even number equals an odd number.

    An odd number plus an odd number equals an even number.

    0 + 1 = odd number

    0 + 2 = even number, 2 is not odd, so zero must be even.

  16. Tam/WB2TT

    Tam/WB2TT Guest

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

  17. No, it most certainly is *not*. [sin(x)]/x for x=0 is
    0/0 and is undefined. The *limit as x approaches 0* of
    [sin(x)]/x is 1, but that's not even vaguely the same
    thing. The difference is huge.
    Christopher Mattern

    "Which one you figure tracked us?"
    "The ugly one, sir."
    "...Could you be more specific?"
  18. In the days before IEEE format, at least one FORTRAN was designed to
    read, write, and test equality on -0.0, so that it could be used as NaN
    (usually for "datum missing"), but I grant that having a real NaN is
    ever so much nicer.
  19. How about the following:

    (2 * 0) / 0 = (2 * 0) * (1 / 0 ) <- Definition of division as the
    inverse of multiplication
    (2 * 0) * (1 / 0) = 2 * (0 * (1 / 0)) <- Associative property of
    2 * (0 * (1 / 0)) = 2 * (0 / (0 / 1)) <- Definition of division
    2 * (0 / (0 / 1)) = 2 * (0 / 0) <- 0 / 1 = 0

    He was just leaving out some unnecessary steps, being as that they are
    rather common and generally just understood.

    Of course, this is following the same strange assumptions of the fact that 0
    / 0 is a defined operation, or that 0 has an inverse.
  20. Nick Atty

    Nick Atty Guest

    [huge cross-posting continued remorselessly - fu to rec.puzzles 'cos
    that's where I read it]

    Someone, and I can't remember who, once said something to the effect
    that all computer programs should work like this. They should allow no
    instances of something, one instance of it, or any number at all.

    It's not a bad idea - think how many bugs are a result of programs
    dealing with far more things than the programmer ever expected.

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

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