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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

$x\in R$. The archimedean property furnishes a positive integer $m_1$ s.t. $m_1.1>x$.

Apply the property again to get another positive integer $-m_2$ s.t. $-m_2.1>-x$.

Now, we have $-m_2<x<m_1$.

I stopped here, I know there exists an $m\leq m_1$ s.t. $m-1<x<m$, but I don't know how to continue.

Any help is appreciated!