Proof: Convergent Sequences are Cauchy | Real Analysis

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We prove that every convergent sequence is a Cauchy sequence. Convergent sequences are Cauchy, isn't that neat? This is the first half of our effort to prove that a sequence converges if and only if it is Cauchy. Next we will have to prove that Cauchy sequences are convergent! Subscribe for more real analysis lessons!

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Wow, I just love the clarity of your work. Nothing is assumed, no step is deemed too simple that it doesn't need to be explained. Thanks for making the vids!

rmw
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HI
This video is great. I would suggest that the original sequence (a_n) would be written as (a_k) to avoid confusion

ahmedalosais
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The use of if and only if seems inappropriate to me as you here only proved one way and that is I think the only possible way as there are Cauchy sequences that do not converge. Cauchy would thus be a weaker notion than convergence in my mind. Do not take my word gor it

deisandmis