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Prove if that $0

The question states to use the Archimedean Property; If $a,b \in \mathbb{R}$ where $a < b$, then there exist an $n \in \mathbb{N}$ such that $b

My guess is to begin with the result of the Archimedean Property ($b

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    You could apply the Archimedian Property to $b$ and $1$... – 2017-02-18
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    Show that an $n$ exists for each situation, and then consider the maximum of the two. – 2017-02-18

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I'll get you started. Using el_tenedor's comments: Consider $b$ and $1$. By the Archimedean Property, there exists $N\in\mathbb{N}$ such that $b

Here, we've assumed that $a<1$ and $b>1$, by the way. That is also something you'll need to work around.

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    @J.Jones did you find this useful? – 2017-02-20