Youtor
Intro to Cauchy Sequences and Cauchy Criterion Real Analysis
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=VNoHcFoawTg
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: • Proof: Cauchy Sequences are Bounded |... • Proof Convergent Sequences are Cauchy: • Proof: Convergent Sequences are Cauch... • Proof Cauchy Sequences Converge: • Proof: Cauchy Sequences are Convergen... • #Math #RealAnalysis • ★DONATE★ • ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons • ◆ Donate on PayPal: https://www.paypal.me/wrathofmath • Thanks to Robert Rennie and Barbara Sharrock for their generous support on Patreon! • Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ • Follow Wrath of Math on... • ● Instagram: / wrathofmathedu • ● Facebook: / wrathofmath • ● Twitter: / wrathofmathedu • My Music Channel: / @emery3050
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