MATH 242: Analysis 1 (McGill Final)

Currently Playing: Show Function Limit Doesn't Exist with Sequences | 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/45kcMjq We introduce a sequential divergence criterion for functional limits. We previously proved that the limit of a function f(x) converges to L as x approaches c if and only if f(a_n) converges to L for every a_n converging to c but with terms not equal to c. The contrapositive states that if we can find two sequences a_n and b_n converging to c, but where f(a_n) and f(b_n) do not converge to the same thing - then the limit of f(x) as x approaches c does not exist. #realanalysis Epsilon-Delta Definition of the Limit of a Function: https://youtu.be/kVQNhAIFZYc Connecting Function Limits and Sequence Limits: https://youtu.be/7svyCaVjH6w ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu