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Difficult Analysis proofs

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Let x, y, and z be real numbers. Prove the following:

    1. If x * z = y * z, then x = y.

    2. If x is not equal to 0, then x^2 > 0. (consider the two cases x > 0 and x < 0 ).

    3. 0 < 1

    4. For each n ∈ N, if 0 < x < y, then x^n < y^n

    5. If x > 1, then x^2 > x.

    6. If 0 < x < 1, then x^2 < 1

    7. If 0 < x < y, then 0 < √x < √y

    8. If x > 0, then 1/x > 0. If x < 0, then 1/x < 0.

    9. If 0 < x < y, then 0 < 1/y < 1/x.

    10. If xy > 0, then either (i) x > 0 and y > 0, or (ii) x < 0 and y < 0.


    2. Relevant equations

    Ordered Field Axioms


    3. The attempt at a solution

    Need help with these
     
  2. jcsd
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