MATH 242: Analysis 1 (McGill Final)

Currently Playing: Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis

Support the production of this course by joining Wrath of Math to access all my real analysis videos plus the lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Get the coolest math clothes in the world! https://mathshion.com/ Real Analysis course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook! https://amzn.to/3CMdgjI 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! #RealAnalysis 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 Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu