Proof: Limit Law for Sum of Convergent Sequences | Real Analysis

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We prove the limit law for the sum of convergent sequences. If a_n converges to a and b_n converges to b, then the sequence a_n + b_n converges to a + b. As in, the sum of convergent sequences converges to the sum of their limits. This is a fairly straightforward proof using the epsilon definition of a convergent sequence.

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Комментарии
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Hello, just wanna ask, in 5:03 how did you arrive at ε/2? Thanks :)

joshtumacay
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Great videos! Suggestion - Maybe if you add a number prefix in the title of the video, it would make it easier to follow from one to another in an optimal sequence and also help categorize them in sub-topics.

christian.adriano
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Excellent video! Other proofs for this concept online (and in my my notes) did not go into nearly as much detail behind the rationale for the steps👍

laith
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Hey, great video! Are there videos for the multiplication and division like this one?

martin_skachkov
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You have offered a really nice proof. Thank you so much!

jingyiwang
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