(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I understand everything except the last two lines. I am really confused about the last two lines of the proof. (actually I was never able to fully understand it since my first year calculus)

I agree that if ALL three of the conditions n≥N, k≥K, and n_{k}≥N are satisfied, then the last line is true. But why does the condition n≥N alone imply that the last line is true? Does n≥Nguaranteethat k≥K, and n_{k}≥N?

Why is it true that n≥N => |a_{n}-a_{n_k}| < ε/2 ?

And why is it true that n≥N => |a_{n_k}-L| < ε/2 ?

Can somebody kindly explain the last two lines of the proof in more detail?

2. Relevant equations

N/A

3. The attempt at a solution

N/A

Any help is much appreciated!

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# Homework Help: Every Cauchy sequence of real numbers converges

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