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Homework Help: Prove that there is no positive real

  1. Mar 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove that there exists no smallest positive real number.
    3. The attempt at a solution
    Lets assume for contradiction that x is the smallest positive real.
    Now we will look at the midpoint between 0 and x which is x/2, well x/2 is positive and smaller than x so this is a contradiction, so there is no smallest positive real.
  2. jcsd
  3. Mar 26, 2014 #2


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    Looks fine to me. If you want to be pedantic, you may want to prove explicitly that ##x/2## is positive and strictly less than ##x##.
  4. Mar 26, 2014 #3
    Depending on how much rigor you need to put in, you might want to prove ##0<\frac{x}{2}<x##. I know it's trivial, so perhaps it's not needed.
  5. Mar 26, 2014 #4
    ok thanks, it almost seemed to easy just wanted to make sure it worked.
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