We prove the sequence {1/n} is Cauchy using the definition of a Cauchy sequence! Since (1/n) converges to 0, it shouldn't be surprising that the terms of (1/n) get arbitrarily close together, and as we have proven (or will prove, depending where you're at), convergence and Cauchy-ness are equivalent, so (1/n) is Cauchy - let's prove it! #RealAnalysis
Besides the definition of Cauchy, the only thing we need is the Archimedean principle, proven here: • Proof: Archimedean Pri...
Intro to Cauchy Sequences: • Intro to Cauchy Sequen...
Cauchy Sequences are Bounded: • Proof: Cauchy Sequence...
Sequence is Cauchy iff it is Convergent: • Proof: Sequence is Cau...
Real Analysis playlist: • Real Analysis
Real Analysis Exercises: • Real Analysis Exercises
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13 окт 2024