Theorem 1.21 Rudin. Obviously wrong stated, right?

[saim_]

Theorem 1.21 Rudin. Obviously wrongly stated, right?

Theorem 1.21 in Rudin states:

For every real $x > 0$, and every integer $n > 0$, there is one and only one real $y$ such that $y^{n} = x$.

The bold part should be "only one positive real", shouldn't it, or am I missing something? The proof also start with with an implicit assumption that $y$ is positive.

 

[superg33k]

Yeah I agree it should be positive.

The obvious counter example if it wasn't is n=2 then both -1^2=1 and 1^2=1 making the statement false.

 

[GenePeer]

I'm looking at the Third Edition and it says "one and only one positive real."

 

[saim_]

Thanks guys.

@GenePeer: I got third edition as well and it says exactly what I wrote. The error must be only in some prints then.