Thread: Ordered Fields

Alright so I'm not sure if this is the right thread for this, but this is the proof i need help with:
Let S be an ordered field and suppose x, y ∈ S. Using only the Ordered Field axioms, show that 0<x<y implies 0<(1/y) <(1/x).

I just need a starting point to go from but i'm stuck at defining that 1/y and 1/x are both elements of S

By definition of a field, and exist because are nonzero. What happens if you multiply all of by ?

You also need, of course, "if 0< x then 0< 1/x". Have you already proved that?