# Help with Quantifiers

• August 27th 2012, 09:55 AM
JoannaEris
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 thatAttachment 24612

I'd appreciate any help.
• August 27th 2012, 10:33 AM
emakarov
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.
• August 27th 2012, 11:16 AM
Plato
Re: Help with Quantifiers
Quote:

Originally Posted by JoannaEris
Prove or give a counterexample to the following statement: For each positive integer a, there exists a positive integer b such thatAttachment 24612

Is there a solution if $a=3~?$