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Analysis problem

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Given x > 0 and [tex]n \in N[/tex], prove that there is a unique y > 0 s.t. [tex]y^n = x[/tex] exists and is unique

    2. Relevant equations
    Hint is given: consider [tex]y = 1. u.b. \{s \in R : s^n < x\} [/tex]

    3. The attempt at a solution
    I'm not used to this style of proof (real analysis I), help would be appreciated, thanks. BTW, what does "u.b." signify?
  2. jcsd
  3. Jan 26, 2010 #2


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    It's actually l.u.b. with a letter "L" instead of a digit "1". It means "least upper bound. Does that help?
  4. Jan 27, 2010 #3
    oh, now its clearer. thanks
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