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Math Help - How to prove this, ordered fields

  1. #1
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    How to prove this, ordered fields

    If x != 0, then 1/(1/x) = x.

    I know by m5 you can rewrite as:

    1/(x^{-1}) = x.

    Im not quite sure how to proceed here however, I thought using m2 would help for this, but im not sure how I should show that \frac1{x^{-1}} (x) = x^{2}
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  2. #2
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    Quote Originally Posted by p00ndawg View Post
    If x != 0, then 1/(1/x) = x.
    I know by m5 you can rewrite as: 1/(x^{-1}) = x.
    \frac1{x^{-1}} (x) = x^{2}
    You have us at a disadvantage. We donít have your set of axioms.

    But this may help. \frac{1}{\displaystyle\frac{1}{x}}=\left(\frac{1}{  x}\right)^{-1}=\left(x^{-1}\right)^{-1}=x.

    You can apply the correct axioms to that.
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