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Equivalence problem

  1. Mar 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Are the statements A and B equivalent with each other?

    A. Suppose that n is an integer which is not a perfect square.
    B. If n >= 1, then [tex]\sqrt{n}[/tex] is either an integer or is irrational.

    3. The attempt at a solution
    I am keen on saying that the two statements are not equivalent.
    However, Oxford's undergraduate booklet claims that they are equivalent.

    In my opinion, A is inclined to that n is not a perfect square, while B is neutral.
     
  2. jcsd
  3. Mar 3, 2009 #2
    they are quite different. Statement 1, is an assumption (which we are assuming to be true), whereas statement 2 is a...well its a statement (that may be true/false)

    Also, consider the second statement

    It says sqrt(n) is either integer or irrational. This means sqrt(n) could be sqrt(2/3) which is also irrational. However, it is not equivalent to saying n is an "integer" and not a perfect square..

    edit: ok, Statement 2 also says n>=1(missed that) so just do the entire same argument for sqrt(3/2), that'll also hold
     
  4. Mar 3, 2009 #3
    they are quite different. Statement 1, is an assumption (which we are assuming to be true), whereas statement 2 is a...well its a statement (that may be true/false)

    Also, consider the second statement

    It says sqrt(n) is either integer or irrational. This means sqrt(n) could be sqrt(2/3) which is also irrational. However, it is not equivalent to saying n is an "integer" and not a perfect square..
     
  5. Mar 3, 2009 #4
    I agree with you.
     
  6. Mar 3, 2009 #5
    Do you mean that the two statements are equivalent?
     
  7. Mar 3, 2009 #6
    No he still means they are not equivalent. Just plug in 3/2 instead of 2/3 in his previous argument of why they are not equivalent.
     
  8. Mar 3, 2009 #7
    Thank you both!
    The problem is now clear.
     
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