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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 intersection of an arbitrary collection of closed sets is closed, and the union of a finite collection of closed sets is closed. To do this, we use DeMorgan's Laws, the definition of closed and open sets, and previously proven results on the unions and intersections of open sets. #RealAnalysis DeMorgan's Laws: https://www.youtube.com/watch?v=-LW2lGHv0GE Intro to Open Sets: https://youtu.be/pnWgj8jjs3w Proof for Unions and Intersections of Open Sets: https://www.youtube.com/watch?v=5tiKwVmEglA All About Closed Sets: https://www.youtube.com/watch?v=O3ECYp4ICFA ★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