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 Dec22 comment Dubiety About An Inequality Proof Whoops, he specifies that $xy > 0$ if $x \in F$, $y \in F$, where $F$ is an ordered field, and $x >0$ and $y > 0$...I reckon more careful reading elucidates all answers... Dec22 asked Dubiety About An Inequality Proof Dec19 awarded Constituent Dec15 awarded Famous Question Dec9 awarded Caucus Dec7 awarded Famous Question Dec6 awarded Notable Question Dec2 awarded Popular Question Nov30 awarded Popular Question Nov22 comment Four Isosceles Trapezoids Oh, wait! When I wrote the problem statement, I forgot to write that $x$ and $y$ are assumed to be positive integers. How does that change things? Could I immediately infer that $\displaystyle A = \frac{y+x}{2} \cdot \frac{y-x}{2}$ means that $A$ has to be factored into two positive integers? Nov17 comment Four Isosceles Trapezoids I do not understand why I have to argue that $\frac{y+x}{x}$ and $\frac{y-x}{2}$ must be integers. I want them to be integers, so I compel them to be integers; and for each fraction to evaluate to an integer, the numerator must be some multiple of $2$. Is this the sort of proof you had in mind? If not, I do not see how it is possible to prove that they must be integers. Nov15 awarded Notable Question Oct23 awarded Popular Question Oct19 awarded Notable Question Oct7 awarded Notable Question Oct5 awarded Yearling Oct1 awarded Notable Question Sep24 awarded Autobiographer Sep22 awarded Taxonomist Sep15 accepted The role of 'arbitrary' in proofs