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Math Help - Problem of Dividing By Zero Solved

  1. #16
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by topsquark View Post
    Pffl. If they can teach "intelligent design" in schools why can't they teach this? More garbage for them to have to "unlearn" at some point.

    -Dan
    Pffl. If they can teach "evolutionism" in schools why can't they teach this? More garbage for them to have to "unlearn" at some point.

    -Quick
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  2. #17
    Senior Member OReilly's Avatar
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    Is that "nullity" theory somewhere officialy published?
    On that BBC site there is an answer of that proffesor on many posts that he will provide more proofs soon, which left me with doubt whether he actually did fully define that theory or did he just wanted publicity!
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  3. #18
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick View Post
    Pffl. If they can teach "evolutionism" in schools why can't they teach this? More garbage for them to have to "unlearn" at some point.

    -Quick
    At least evolution is a scientifically testable theory. I have yet to hear anyone come up with a testable version of intelligent design. (And by its very nature I can't think of a way to do it.)

    -Dan
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  4. #19
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    Here is something that would help you understand why division by zero is undefined.

    a/b=ab^{-1}
    Where, b^{-1} is the unique solution to,
    bx=xb=1.
    Where, 1 is the unique element such that,
    c1=1c=c.

    Now,
    a/0=a0^{-1}
    Thus, we 0^{-1} is unique solution to,
    0x=1.
    But, that is not possible.

    The reason that is not possible is because,
    0x=(1-1)x=x-x=0
    Thus any element multiplied with zero is zero.
    Thus there is no solution to the equation above.
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  5. #20
    Grand Panjandrum
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    Quote Originally Posted by OReilly View Post
    I was surprised that officials let him do that.

    I don't think that theory that hasn't been accepted by all or at least majority of math community should be learned in schools!
    Consensus is an irrelevance in Maths, now consistency ..

    RonL
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  6. #21
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    Quote Originally Posted by ThePerfectHacker View Post
    Here is something that would help you understand why division by zero is undefined.

    a/b=ab^{-1}
    Where, b^{-1} is the unique solution to,
    bx=xb=1.
    Where, 1 is the unique element such that,
    c1=1c=c.

    Now,
    a/0=a0^{-1}
    Thus, we 0^{-1} is unique solution to,
    0x=1.
    But, that is not possible.

    The reason that is not possible is because,
    0x=(1-1)x=x-x=0
    Thus any element multiplied with zero is zero.
    Thus there is no solution to the equation above.
    Think of it this way nan (or if you must nullity (yuck, yuck ,,))
    is a symbol for undefined.

    RonL
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  7. #22
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    Quote Originally Posted by CaptainBlank View Post
    Think of it this way nan (or if you must nullity (yuck, yuck ,,))
    is a symbol for undefined.
    That is not a definition.

    A "symbol" represents an element from some set. There is no such set.
    ----
    Maybe, what you are saying is useful in computer science. But I do not know.
    Last edited by ThePerfectHacker; December 8th 2006 at 08:17 AM.
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  8. #23
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker View Post
    That is not a definition.

    A "symbol" represents an element from some set. There is no such set.
    You seem to be lacking in imagination today.

    We would be talking here of another version of the extended reals with
    three ideal elements added +inf, -inf, nan. That makes nan an element
    of the \mathbb{S} \rm{uper} \mathbb{E} xtended \mathbb{R} eals^{(tm)}.

    ----
    Maybe, what you are saying is useful in computer science. But I do not know.
    Why are we interested in number at all if not because of its usefullness
    in games and puzzles?

    Also, alarm bells should be sounding in your head as you type that statement.
    If it were usefull then maths should look at it as usefull tricks in computation
    always should be of interest to maths.

    RonL
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  9. #24
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    Quote Originally Posted by CaptainBlack View Post
    We would be talking here of another version of the extended reals with
    three ideal elements added +inf, -inf, nan. That makes nan an element.
    Such a defintion, is mathematically acceptable.

    However, what are the binary operations on this set?*)
    I am willing to bet whatever they do not even turn this set into a ring.

    *)That is the only thing you must do for me, otherwise, I cannot accept this defintion.**)

    **)And if they are none, for these elements. What is even the purpose in defining such elements, it does not even form a monoid! Or whatever you call it.
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  10. #25
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    Quote Originally Posted by ThePerfectHacker View Post
    Such a defintion, is mathematically acceptable.

    However, what are the binary operations on this set?*)
    I am willing to bet whatever they do not even turn this set into a ring.

    The operations are +, -, *, / as normal. With:

    <br />
nan \circ x =nan<br />

    <br />
x \circ nan =nan<br />

    for all x \in \mathbb{SER} where \circ denotes
    any of the operations.

    It's my job here to point out that this might be a structure of interest
    not to show what existing type of structure it is.

    *)That is the only thing you must do for me, otherwise, I cannot accept this defintion.**)

    **)And if they are none, for these elements. What is even the purpose in defining such elements, it does not even form a monoid! Or whatever you call it.
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  11. #26
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    Quote Originally Posted by CaptainBlack View Post
    The operations are +, -, *, / as normal.
    I do not know what you are using, but - and / are not binary operation.
    They represent the inverse operation of + and *.
    In the way I defined them above.

    So I am going to pretend you did not mention the - and / and work with * and +.



    You did not define the binary operation between inf and -inf and its elements.
    Last edited by ThePerfectHacker; January 2nd 2007 at 10:53 AM.
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  12. #27
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    Quote Originally Posted by ThePerfectHacker View Post
    I do not know what you are using, but - and / are not binary operation.
    They represent the inverse operation of + and /.
    In the way I defined them above.

    So I am going to pretend you did not mention the - and / and work with * and +.



    You did not define the binary operation between inf and -inf and its elements.
    I dont need to these are inherited from the extended reals.

    RonL
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  13. #28
    Senior Member TriKri's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    a/b=ab^{-1}
    Where, b^{-1} is the unique solution to,
    bx=xb=1.
    Where, 1 is the unique element such that,
    c1=1c=c.

    Now,
    a/0=a0^{-1}
    Thus, we 0^{-1} is unique solution to,
    0x=1.
    But, that is not possible.

    The reason that is not possible is because,
    0x=(1-1)x=x-x=0
    Thus any element multiplied with zero is zero.
    Thus there is no solution to the equation above.
    But 0\cdot \infty is undefined. And if we define \frac{1}{0}\ =\ 0^{-1} to be +\infty, then x - x\ =\ \infty - \infty would be undefined too, not zero.
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  14. #29
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    Quote Originally Posted by TriKri View Post
    But 0\cdot \infty is undefined. And if we define \frac{1}{0}\ =\ 0^{-1} to be +\infty, then x - x\ =\ \infty - \infty would be undefined too, not zero.
    You are assuming this algebra structure (and I believe you are reffering to the Extended Reals) is a ring, that is distribution is true. It does not work anymore.

    Furthermore, in what I said, all elements have binary operations with each other. Over here not all do (that is some are not defined). So there is no problem.
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  15. #30
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    I just have to go off in defense of intelligent design really fast:

    intl. design is NOT:

    1. religous. People in all sorts of religions stand with this theory.
    2. philisophical. Intl. design proponents are very careful to attatch no description of what intelligence made us to the theory.
    3. unscientific. The theory has come up with a way of quantatively telling whether inteeligence made something or not and many proven scientific theories support, through that method, the idea of intl. design.

    Is it right? No one knows for sure. Is evolution right? No one knows that, either.

    ANYWAY:

    It pains me to think about what the proffesor was doing. He is either really, really out of it or is so egotisical he deserves a world record. Either way, he should be put in a mental hospital .
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