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Basically what I need is to know if this proof is correct

what I need to prove is:
if $a^3 > a $ then $a^5>a$ so, what i did was this:
$a^3 a^2 > a a^2$
$a^5 > a^3$
because $a^5>a^3$ I can say that $a^5>a$

EDIT: $a,b \in \mathbb{R}$, sorry I totally forgot to write it

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    It would be good to specify the context: Do you want a proof for the case that $a$ is a real number? Do you want it for the case of arbitrary [ordered fields](http://en.wikipedia.org/wiki/Ordered_field)? If it's not the latter, tagging [tag:abstract-algebra] is perhaps not the most suitable tag. I guess [tag:algebra-precalculus] or [tag:inequality] would be better. \\ This in fact doesn't really matter to the way it's proved, but I think it's good to state your assumptions whenever you post a question.2012-01-11

3 Answers 3