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Math Help - Help with Quantifiers

  1. #1
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    Help with Quantifiers

    Can someone help me? I'm stuck with this:

    Prove or give a counterexample to the following statement: For each positive integer a, there exists a positive integer b such thatHelp with Quantifiers-ecuacion.png

    I'd appreciate any help.
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  2. #2
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    Re: Help with Quantifiers

    \frac{1}{2b^2+b}<\frac{1}{ab^2} iff 2b^2+b>ab^2. In the latter inequality, both sides are quadratic polynomials in b. I understand that this problem is formally about quantifiers, but essentially it is about comparing two quadratic functions. For this reason, if you need help with this, it would make sense to post the problem to pre-university Algebra or Pre-calculus subforums.
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  3. #3
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    Re: Help with Quantifiers

    Quote Originally Posted by JoannaEris View Post
    Prove or give a counterexample to the following statement: For each positive integer a, there exists a positive integer b such thatClick image for larger version. 

Name:	Ecuacion.png 
Views:	1 
Size:	4.3 KB 
ID:	24612
    Is there a solution if a=3~?
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