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Analysis proof

  1. Sep 14, 2006 #1

    kreil

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    Gold Member

    Prove that if b is greater than or equal to zero (b in R), there exists a non-negative real number x such that x2=b.

    I really don't know where to go. I think I need to modify a proof done in a class that I missed, so if someone could just give me a few hints I'll fill in the rest.

    Thanks
    Josh
     
  2. jcsd
  3. Sep 14, 2006 #2

    AKG

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    How have you defined the reals?

    Or maybe prove that on [0, infinity), the function x -> x2 is continuous, increasing, and unbounded, and apply intermediate value theorem.
     
    Last edited: Sep 14, 2006
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