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Theorem 1.21 Rudin. Obviously wrong stated, right?

  1. Aug 1, 2011 #1
    Theorem 1.21 Rudin. Obviously wrongly stated, right?

    Theorem 1.21 in Rudin states:

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

    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 [itex]y[/itex] is positive.
     
    Last edited: Aug 1, 2011
  2. jcsd
  3. Aug 1, 2011 #2
    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.
     
  4. Aug 1, 2011 #3
    I'm looking at the Third Edition and it says "one and only one positive real."
     
  5. Aug 1, 2011 #4
    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.
     
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