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Is zero even or odd?

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

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  1. vonroach

    vonroach Guest

    No it is meaningless gibberish.
     
  2. vonroach

    vonroach Guest

    Confused is too mild a term. If y = 1/x. then y goes from1 to a very
    small fraction as x increases from 1. If x decreases to small
    fractions, then y increases. x=0 yields a meaningless result.
     
  3. vonroach

    vonroach Guest

    There isn't one. Division by 0 is meaningless.
     
  4. vonroach

    vonroach Guest

    Both are meaningless. Just crap piled higher and deeper as in Ph D.
     
  5. Wow! We started from the trollish "Re: Is zero even or odd?" and now
    we're arriving to Lie (news)groups...
    ;-)


    Michele
     
  6. vonroach

    vonroach Guest

    yes
     
  7. vonroach

    vonroach Guest

    x^0 = 1 except when x=0 which doesn't exist.
     
  8. John Fields

    John Fields Guest

    ---
    And there's the rub! My point is that it _should_ be defined, and
    defined like this:


    0 1
    --- = 1, --- = oo,
    0 0
    ---
    ---
    I disagree.


    If we say

    x
    y = lim --- = 1
    x +oo -> -oo x

    Then y will be equal to 1 for every instance of x except when x
    crosses over from + to -?

    In my view that's preposterous, and the mere parroting of "division by
    zero is disallowed because it's undefined" a convenient dodge. No
    insult intended.[/QUOTE]

    It is desirable for mathematics not to allow two contradictory
    statements such as 0/0=1 and 0/0=2 to be true at the same time; and your
    resoning allows these statements to be true in some cases (we did this
    in the Ohm's law episode, where you never said my reasoning was wrong,
    it was merely not the thing you wanted to prove).[/QUOTE]

    ---
    Actually, what I didn't want to do was to get into a long, off-topic
    harangue about Ohm's law (Ohm's formula, actually. Ohm's law is an
    entirely different thing and is used to determine whether conductors
    are 'Ohmic'. That is, if their resistance remains constant when
    current through them is made to vary), which requires that for
    resistance to be _measured_ a known voltage _must_ be placed across it
    and the resulting charge flowing through the resistance determined.
    Your example eschewed the _practical_ requirements in order to
    contrive a desired outcome and, as such, was irrelevant.

    But, proceeding along that tack for a while, maybe we can use our
    "exquisite" technology to advantage here by assuming that we have
    managed to craft two identical zero ohm resistors (superconducting, if
    you like) and that we can force equal numbers of electrons through
    each of them in equal amounts of time. Then, since Q = It, the
    current flowing in each resistor will be I = Q/t, and the ratio of the
    currents will be I1/I2.

    Since Q/t will be identical for both resistors, I1/I2 will be 1 for
    any current. Now, let's say that we inject fewer and fewer pairs of
    electrons per unit time into the 'rig' and that eventually we inject
    none. Since we have agreed that as long as I1=I2 then I1/I2 will be
    equal to 1, does 0/0 not satisfy that requirement?
    ---
     
  9. I'll take that as a "No" then.

    George
     
  10. [/QUOTE]

    That is incorrect, multiplication and division
    are of equal precedence.
    Not at all. I have avoided writing this as a limit
    for the reason Mati gives but will follow your lead
    Let

    k*x
    y(x) = ---
    x

    Clearly y(x) = k for all non-zero finite values of x and

    limit y(x)
    x->0 ---- = k
    x

    By your argument that the limit can be used to
    define the value at zero, we can infer:

    y(0)
    ---- = k
    0

    but of course y(0) = 0 hence

    0
    --- = k
    0

    for all finite k.

    George
     
  11. And that's nonsensical.

    It gives us, for example,
    1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2

    Well, so you are talking inconsistent nonsense. You must not expect
    that it will impress anybody much.
    This notation is complete and utter meaningless hogwash. What you
    _can_ say is that

    lim (x->v) (x/x) = 1

    for _all_ v in R (and actually also if v is +oo or -oo, which is not a
    number, but a neighborhood in some sense of the word).

    But you can equally well say that

    lim (x->v) (2*x/x) = 2

    for _all_ v in R. For v=0, both limits are of the _form_ 0/0, and
    that means that any such limiting _form_ is undefined without further
    qualification. But you don't need limiting arguments to show that 0/0
    can't be defined: mere algebra is sufficient.
    Your notation above is rubbish to start with, so assigning any meaning
    to it is likely to be rubbish too.
    Well, not being able to choose a consistent value is _the_ perfect
    reason for leaving it undefined. You call it a dodge, other's call it
    a necessity.
     
  12. I read in sci.electronics.design that John Fields <[email protected]
    I think this thread has shown that there are two sorts of people, those
    that associate taboos with 0 and those that don't.

    My view is that logically-inferred values of expressions involving zero
    should be accepted unless they result in contradictions. I do not
    support a priori restrictions on interpretation, and I do not accept
    that 'undefined' is a valid show-stopper.
     
  13. I read in sci.electronics.design that George Dishman
    Yes. John Fields' value of 1 is just ONE valid solution. Not wrong, but
    not the whole solution.
     
  14. 'Undefined' is a human artefact. Anything can be defined; if the
    definition results in contradictions, it's a bad definition.
    0/0 can't be *defined* as 1 because, as has been repeatedly
    demonstrated, that definition results in contradictions, such as the one
    illustrated above.

    The only definition that does not result in contradictions is that 0/0
    is 'any number'. 1 is just one solution.
     
  15. John Fields

    John Fields Guest

    ---
    I thought that by interspersing your remarks among mine you were being
    arbitrary. I see now that wasn't the case; thanks.
    ---
    ---
    I disagree. All I was trying to do was to set up the initial
    conditions to give me an equal numerator and denominator as a starting
    point for a proof that, eventually, 0/0 = 1.
    ---
    ---
    0/0 would still be = 1 but yes, of course, to the rest of it. A
    _measurement_ would be impossible without a known, non-zero voltage
    forcing charge through the resistance.
    ---
    ---
    Yes, thanks.
    ---
    ---
    OK, but it seems to me that if you subscribe to

    2r
    x = lim ---- = 2
    r->0 r

    when r = 0, then 0/0 _must_ be equal to 1, otherwise x could not have
    been equal to 2. That is, if r/r = y and 2y = 2, then y = 1.
    ---
    ---
    Because it doesn't?

    In the latter case we're trying to determine whether, when equal
    quantities are divided into each other, the result will always be
    equal to 1, while in the former we're dealing with with the interplay
    between physically different entities. I.e., 1 apple/1 orange = ???
     
  16. So what do you do when there are multiple logically-inferred values,
    as with 0^0? Or when the logically-inferred value breaks a lot of
    other things, as with 0/0.

    BTW, what's log 0? arctan 0?
     
  17. John Fields

    John Fields Guest

    ---
    In the context of the problem at hand, the definition of division
    isn't in question. What's being discussed is whether zero, being
    equal to itself will yield a quotient of 1 when it's divided into
    itself. As for the rest of it, I will follow the advice you proffer
    in your dotsig and forego arguing with you.
     
  18. John Fields

    John Fields Guest

     
  19. John Fields

    John Fields Guest

     
  20. George Cox

    George Cox Guest

    No 0/0 is undefined, it has _no_ value.
     
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