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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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?
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