MATH 242: Analysis 1 (McGill Final)

Currently Playing: A Set is Closed iff it Contains Limit Points | 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 prove the equivalence of two definitions of closed sets. We may say a set is closed if it is the complement of some open set, or a set is closed if it contains its limit points. These definitions are equivalent, so we'll prove a set is closed if and only if it contains its limit points. To do this we use contradiction for the forward direction, then to prove a set containing its limit points implies it is closed - we use the contrapositive, meaning we prove that if a set is not closed then it doesn't contain all of its limit points. #realanalysis Open Sets: https://youtu.be/pnWgj8jjs3w Closed Sets: https://youtu.be/O3ECYp4ICFA Limit Points: https://youtu.be/RmsvftFNMtE ★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