Division by zero. Go ahead and laugh.

Discussion in 'Undergraduate Math' started by Lefty, Oct 7, 2004.

  1. Lefty

    Lefty Guest

    Thanks. I suppose you're probably right.

    If you're feeling at all sympathetic you could help me out by weighing in
    and straightening me out a little.
     
    Lefty, Oct 8, 2004
    #41
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  2. Lefty

    Lefty Guest

    There are no paradoxes or inconsistencies in mathematics, unless you
    remove


    Thanks Dave, but the reference to JH, now that stings a little.

    OK, x+3=0. No solution. No problem. Is this a singularity for addition on R
    ? I honestly dont know.

    I'm _not_ saying that 1/0 = infinity. All I am saying is that leaving it
    "undefined" is the equivalent of waving magic wands. I dont think that it's
    good at all.

    What I said what that 1 / 0 = [inconsistency] or 1 / 0 = [paradox] ,
    or something to that effect.


    Trying to gain some focus here so bear with me please.

    Thanks.
     
    Lefty, Oct 8, 2004
    #42
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  3. Lefty

    Lefty Guest

    Division by zero creates an inconsistency in arithmetic, and any result
    can

    I'm saying that it seems that there is something being missed by leaving it
    "undefined".

    If 1/0 => [inconsistency], then there should be a formal language or
    symbology to state that when you divide by zero you get a paradox or an
    inconsistency. There should be some way of stating this formally using
    _algebra_ . Not paragraphs of english. Algebra would be more complete, and
    the whole thing might lead to new knowledge.

    I'm guessing, but it's all just fun.
     
    Lefty, Oct 8, 2004
    #43
  4. Lefty

    Lefty Guest



    It has given me much appreciated insight.

    Numbers are metaphysical entities. They are abstractions. I am not sure if
    these quantities can really be said to exist in the physical universe.
    Obviously they seem to, but this would make an enormous argument.

    However, there are two numbers which seem to fit the physical world almost
    perfectly. Zero and 1. I wont bore you with my musings except to say that
    when considering these numbers, it is almost as if the abstract world is
    bridged to the physical universe by the existence of zero and 1. Zero and 1
    must exist in the real world. It almost resembles the dichotomy of
    existence, true or false.

    Certainly you can have 1 banana. And certainly you can have zero bananas.
    The other numbers are all quite dubious in the real world.

    Might have something to do with why there are singularities. Or maybe it's
    the whiskey talkin' ?

    Who knows.
     
    Lefty, Oct 8, 2004
    #44
  5. One is not "leaving" anything undefined. One is showing that 1/0 cannot
    be defined in a consistent division ring. Just because something that
    looks like a valid alebraic formula can be written, does not mean it is
    a valid algebraic formulate.
    I have already demonstrated this. Now pay attention. 1/0 = x means that
    1 = 0*x. But 0*x = 0, which implies that 1 = 0, which is a
    contradiction. I have just demonstrated exactly what you ask for.
    There should be some way of stating this formally using

    See my previous 3 lines.


    It is no fun to make a pain in the ass of yourself. I have produced the
    demonstration you asked for. Now shut up.

    Bob Kolker
     
    robert j. kolker, Oct 8, 2004
    #45
  6. Just when we thought Plato was dead and buried, you shoed up. Go away.

    Bob Kolker
     
    robert j. kolker, Oct 8, 2004
    #46
  7. Lefty

    N. Silver Guest

    I claim: 1/0 = infinity, 0/0 is an undetermined form,
    and -1/0 = minus infinity.

    However, infinity and minus infinity are not real
    numbers. So, in the real numbers, i.e., those
    numbers in one-to-one correspondence with
    points on the real line, 1/0, 0/0 and -1/0 are
    undefinied.
     
    N. Silver, Oct 8, 2004
    #47
  8. Lefty

    N. Silver Guest

    I claim: 1/0 = infinity, 0/0 is an undetermined form,
    and -1/0 = minus infinity.

    However, infinity and minus infinity are not real
    numbers. So, in the real numbers, i.e., those
    numbers in one-to-one correspondence with
    points on the real line, 1/0, 0/0 and -1/0 are
    undefined.
     
    N. Silver, Oct 8, 2004
    #48
  9. Lefty

    Keckman Guest


    No no. That sounds interesting. Please Lefty tell us more.
     
    Keckman, Oct 8, 2004
    #49
  10. Lefty

    Lefty Guest

    Lefty, you don't know what you are talking about.

    Yes, I know. I'm not arguing that division by zero should be allowed. I am
    arguing that it is not being leveraged. I am arguing that there is a wealth
    of information hidden behind this funky, freaky thing, this contradiction,
    this paradox. I think that there is something mysterious about it which has
    not been revealed.

    Or maybe I just have'nt read enough ? Singularity theory maybe ?
     
    Lefty, Oct 8, 2004
    #50
  11. Lefty

    Lefty Guest


    Thanks Bob, but I think that you took me out of context.
     
    Lefty, Oct 8, 2004
    #51
  12. Lefty

    Lefty Guest



    I believe that the lim 1/x as x->0 is infinity. Am I wrong ?

    Really guys, I'm rusty, so bear with me a little.

    In the above, we're talking about 2 different things however.

    1) Mathematical operations which exist as abstractions, and

    2) Manipulations in the physical world which resemble mathematical things.

    It would be nice to bridge these solidly. Never been done I think,
     
    Lefty, Oct 8, 2004
    #52
  13. Lefty

    Lefty Guest


    I promise that I will not argue about this for the next 5 years. I imagine
    it will probably show up on one of those "usenet crank" websites, who cares.

    I reserve the right to imagine whatever the hell I please. Let freedom
    reign.
     
    Lefty, Oct 8, 2004
    #53
  14. Lefty

    Lefty Guest

    Lets say that you wanted to make a fundamental mathematical statement about
    the physical universe. Please take a look at this axiom. I think that it
    says something about numbers and theri relationship to the physical
    universe.

    Please critique this -

    Maybe I lost my mind, I dont care. Please tell me what you think.

    ----------------------------------------------

    Axiom
    No two objects in the physical universe can ever be identical. Even if they
    are identical in every respect, they still occupy two separate locations,
    again making them different. You can have one of something, and you
    can have zero of something, but that's all, because no two objects can
    ever be identical.

    Proof.
    suppose not,
    contradiction,
    qed,
    bla bla bla
     
    Lefty, Oct 8, 2004
    #54
  15. Gosh, it's very curious then that complex analysis texts which discuss C*,
    the one-point compactification of C, define 1/0. It's truly amazing that
    they do what cannot be done! What a mistake! Will you perhaps take it
    upon yourself to inform the authors of such texts of their horrid error?

    Of course, instead of doing that, it would actually be much more profitable
    for you to think about why you are incorrect in claiming, bluntly, that 1/0
    cannot be defined. (Hint: In systems allowing division of nonzero
    quantities by zero, division is not defined as you have indicated.)

    David Cantrell
     
    David W. Cantrell, Oct 8, 2004
    #55
  16. Hmm. Since you seem to be mentioning "infinity" and "minus infinity" as
    separate entities, it would seem that you're thinking about the two-point
    compactification of R. But 1/0 is normally undefined in that system.

    In the one-point compactification of R, however, we have

    x/0 = unsigned infinity for all nonzero x.

    David Cantrell
     
    David W. Cantrell, Oct 8, 2004
    #56
  17. x = -3.
     
    Richard Henry, Oct 8, 2004
    #57
  18. There is no limit to 1/x as x increases without bound.
     
    Richard Henry, Oct 8, 2004
    #58
  19. Lefty

    Miro Jurisic Guest

    Yes. In order for lim f(x) as x -> a to be defined, the following has to be true:

    For every sequence x1, x2, x3, ... whose limit is a, the limit of sequence
    f(x1), f(x2), f(x3), ... is the same. Then lim f(x) as x -> a is the same as the
    limit of any of those sequences f(x1) etc.

    However, 1/x as x->0 over positive numbers is large and positive, whereas 1/x as
    x->0 over negative numbers is large and negative. This makes lim 1/x as x->0
    undefined.

    For example, consider this sequence of values of x:

    1, -1/2, 1/3, -1/4, 1/5, -1/6, ...

    Clearly, limit of that sequence is zero. Now compute 1/x at those points:

    1, -2, 3, -4, 5, -6, 7, -8, ...

    That is not a convergent sequence. It has no limit.

    meeroh
     
    Miro Jurisic, Oct 8, 2004
    #59
  20. Lefty

    Keckman Guest

    Hey. I'm clad i found "friends" here because i too like to wonder things
    like that.

    I do not agree you. I think what comes to amounts there can only be one.
    That there isn't any something is nothing. It is nonsense. Zero is not a
    number.

    That's why i observe the Naturals starting from number 1, not from zero,
    like
    Peano did.

    But what i think there is: there is true and false, on/off. And sometimes
    those are meaned like numbers one and zero, but in deeper understanding
    they are not.

    In universum something exist. And it's amount is 1. We can't count those
    things that does not
    exist.

    Let's go ahead...If you have any agrees/not agrees, tell.
     
    Keckman, Oct 8, 2004
    #60
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