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Math Help - very puzzled

  1. #1
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    very puzzled

    So I was reading this in a book and just couldn't grasp this...

    It said:
    NOTE
    There is no real number x such that
    0 (multiplied by) x =1 , so 0 has no multiplicative inverse.

    But I thought 0 multiplied by anything was always 0 so how could this be
    no matter what x could be the answer would always be be 0 not 1 right?

    Is it because x isn't a real number? But still that just doesn't seem right.
    please help
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by etherealreaper View Post
    But I thought 0 multiplied by anything was always 0 so how could this be
    no matter what x could be the answer would always be be 0 not 1 right?
    You seem to think you are contradicting the book, but what you say supports what the book says.

    0x = 1 has no solution in the reals because no matter what you choose for x, there is no way to make 0x equal anything other than 0.

    So, there is no value you can multiply 0 by to get 1, hence by definition 0 has no multiplicative inverse.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Philosophic question...

    Is definition of "number" such as x=1/0 can contribute in someway to mathematics?

    (I studied it a bitter, and I came up with the answer "no")
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  4. #4
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Philosophic question...

    Is definition of "number" such as x=1/0 can contribute in someway to mathematics?

    (I studied it a bitter, and I came up with the answer "no")
    Real projective line - Wikipedia, the free encyclopedia
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    Nice! Thank you!
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