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Logical expression using quantifiers

  1. Sep 8, 2007 #1
    1. The problem statement, all variables and given/known data

    Express each statement as a logical expression using quantifiers. State the universe of discourse.:

    There is no smallest positive real number

    3. The attempt at a solution

    (∃y)((∀x)(y<x) )x

    universe of discourse: poaitive real numbers

    Is this correct?

    Thanks
     
  2. jcsd
  3. Sep 9, 2007 #2
    Why not just write: [tex]\forall x > 0,\;\exists y > 0:y < x[/tex]
     
    Last edited: Sep 9, 2007
  4. Sep 9, 2007 #3
    Your statement says that there is a smallest positive number. You want to take the negation of that.
     
  5. Sep 9, 2007 #4
    No, my statement does not say that at all.

    *Edit: If your post was directed at the OP, please state so in your post; else, your assertion is clearly false (your post comes directly after mine, so I assume you are referring to my post)
     
    Last edited: Sep 9, 2007
  6. Sep 9, 2007 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    It is quite possible that ZioX wrote his reply before yours was posted- he thought his would appear immediately after mutzy188's post. Of course, you are right. It would have been clearer if he (and you- your reply might well have wound up after his) had copied the original post into the response.
     
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