# Math Help - 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:

$1/(x^{-1})$ = 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 $\frac1{x^{-1}}$ $(x)$ = $x^{2}$

2. Originally Posted by p00ndawg
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 don’t 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.