# Thread: How to prove this, ordered fields

1. ## How to prove this, ordered fields

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

I know by m5 you can rewrite as:

$\displaystyle 1/(x^{-1})$ = 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 $\displaystyle \frac1{x^{-1}}$$\displaystyle (x) = \displaystyle x^{2} 2. Originally Posted by p00ndawg If x != 0, then 1/(1/x) = x. I know by m5 you can rewrite as: \displaystyle 1/(x^{-1}) = x. \displaystyle \frac1{x^{-1}}$$\displaystyle (x)$ = $\displaystyle x^{2}$
You have us at a disadvantage. We don’t have your set of axioms.

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

You can apply the correct axioms to that.