This is a famous proof that utilizes a common notion.(adsbygoogle = window.adsbygoogle || []).push({});

Theorem. Limits are unique.

let n>N_1 such that blah blah blah is less than epsilon over 2,

let n>N_2 such that blah blah blah is less than epsilon over 2.

For n> max{N_1,N_2},

blah blah blah < blah = epsilon.

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Somebody presented a question today to my professor of why we can't say in the first place,

let n > N such that blah blah blah is less than epsilon over 2, AND!!!

also that blah blah blah is less than epsilon over 2.

Then we skip the max stuff and finish up.

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My professor said this was "ok" and we proceeded. My question is, is this "ok"? and why is it not presented in book then?

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# Regarding epsilon proofs with N1,N2,Max,Min

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