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 integerbsuch thatAttachment 24612

I'd appreciate any help.

Printable View

- Aug 27th 2012, 09:55 AMJoannaErisHelp 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. - Aug 27th 2012, 10:33 AMemakarovRe: Help with Quantifiers
$\displaystyle \frac{1}{2b^2+b}<\frac{1}{ab^2}$ iff $\displaystyle 2b^2+b>ab^2$. 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.

- Aug 27th 2012, 11:16 AMPlatoRe: Help with Quantifiers