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Real Analysis course:    • Real Analysis  
Real Analysis exercises:    • Real Analysis Exercises  

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What are convergent sequences, and what is the definition of the limit of a sequence? We introduce the definitions, with examples and a proof in today's video lesson!

In the definition of the limit of a sequence, we seek to capture what it means for a sequence to get arbitrarily close, or converge, to some limiting value. We do this by using an arbitrarily small "tolerance" value called epsilon. If you're in an analysis class, get ready to write "Let epsilon be greater than 0" an awful lot.

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