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:    • 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