Hi,

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

Thanks for any help with this.

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- April 12th 2009, 02:24 AMZinnersInverse 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. - April 12th 2009, 05:44 AMstapel
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? (Wink)