Proof for Absolute Value of a Convergent Sequence | Real Analysis Exercises

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We prove that if a sequence (a_n) converges to a, then (|a_n|) converges to |a|. That is, if a sequence converges to a finite limit, then the absolute value of the sequence converges to the absolute value of the limit. We prove this using the epsilon definition of the limit of a sequence and the reverse triangle inequality. #RealAnalysis

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Комментарии
Автор

This is an awesome exercise, thank you so very much for making this video.

valeriereid
Автор

Thank you Wrath of Math, excellent video! Very clear and to the point.

Alexakathegrest
Автор

Can I just write my solution as yours for the following question? Let {an} be a sequence. Prove that if {an} converges, then {|an|} converges. I was wondering if I need to proof it differently or not.

aydenzhu
Автор

Thank you for giving hint before proof and also for nice video

farhatfatima