MATH 242: Analysis 1 (McGill Final)

Currently Playing: If Sequence Diverges to Infinity then so do Subsequences | 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 A sequence diverges to infinity if and only if all of its subequences diverge to infinity. We prove this nice result about divergent sequences and divergent subsequences in today's real analysis video lesson by the river! #RealAnalysis #MathOutside The proof proceeds simply with the definition of a sequence diverging to infinity. We only address positive infinity, the negative infinity proof is nearly identical and left as an exercise for the viewer. Definition of Sequence Diverging to Infinity: https://youtu.be/NjpL3IIsEV4 Intro to Subsequences: https://youtu.be/KqX0mKcV_3A Important Fact about Subsequences (n_k \geq k): https://youtu.be/5ZSzzVd9X6U Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu