Thread: Inverse of irrational number

Hi,

How do I prove that the inverse of an irrational number is irrational? I'm stumped.

Thanks for any help with this.

By "inverse", do you mean "reciprocal"? If so, then you might proceed by contradiction:

Assume that x is irrational, with reciprocal 1/x = y. Suppose y is rational, so y = p/q for some integers p and q. Then 1/y = q/p = x, so...

How does that end?