This proof seems amazing. I finally understood it after one hour. (I am slow and not mature)(adsbygoogle = window.adsbygoogle || []).push({});

I have a question though.

In 1.20 (b),

The line that says, "Hence there is an integer m (with -m_{2}[tex]\leq[/tex]m[tex]\leq[/tex]m_{1}) such that...

How does he justify selecting an m in between the two? I feel uncomfortable with this since it is similar to what is being proved, except for the fact that m is an integer.

Is there a Theorem that says we can pick an integer in between two reals?

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# Rudin 1.20 Theorem

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