I have a difficulty in understanding the proof on Rudin's book page 9 regarding the density of Q in R. Specifically, I don't understand this step:(adsbygoogle = window.adsbygoogle || []).push({});

After we prove that there exist two integers [itex]m_{1}[/itex], [itex]m_{2}[/itex] with [itex]m_{1}>nx[/itex] and [itex]m_{2}>-nx[/itex] such that:

[itex]-m_{2}<nx<m_{1}[/itex]

What I don't understand is how from the above get's concludes the following:

Hence there is an integer m (with [itex]-m_{2}≤m≤m_{1}[/itex]) such that:

[itex]m-1≤nx<m[/itex]

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# Proof that Q is dense in R

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