Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis

What are Cauchy sequences? We introduce the Cauchy criterion for sequences and discuss its importance. A sequence is Cauchy if and only if it converges. So Cauchy sequences are another way of characterizing convergence without involving the limit. A sequence being Cauchy roughly means that its terms get arbitrarily close to each other - no limit involved!

We'll see an example of proving a sequence is Cauchy - we prove {1/n} is a Cauchy sequence using the Archimedean property.

Cauchy Sequences are Bounded: https://youtu.be/GulH7nS_65c
Proof Convergent Sequences are Cauchy: https://youtu.be/SubZMuVBajM
Proof Cauchy Sequences Converge: https://youtu.be/xhBfPoSjAR0

#Math #RealAnalysis

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Видео Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis канала Wrath of Math