Proof for Unions and Intersections of Open Sets | Real Analysis
Vložit
- čas přidán 20. 08. 2024
- We prove the union of a collection of open sets is open, and the intersection of a finite collection of open sets is open. To do this, we use basic set operation properties and the definition of open sets. #RealAnalysis
Intro to Open Sets: • Intro to Open Sets (wi...
Real Analysis playlist: • Real Analysis
Real Analysis exercises: • Real Analysis Exercises
◉Textbooks I Like◉
Graph Theory: amzn.to/3JHQtZj
Real Analysis: amzn.to/3CMdgjI
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
Statistics: amzn.to/3tsaEER
Abstract Algebra: amzn.to/3IjoZaO
Discrete Math: amzn.to/3qfhoUn
Number Theory: amzn.to/3JqpOQd
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons
◆ Donate on PayPal: www.paypal.me/...
Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon!
Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: crayonangel.ba...
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● Facebook: / wrathofmath
● Twitter: / wrathofmathedu
My Math Rap channel: / @mathbars2020
Just started this topic in my analysis course. great vid as always
Great video as always!
Thank you!
Is union of finite open sets open?
Is intersection of infinite open sets open?
Another banger by Wrath Of Math
Bangers all day everyday! Really want to get my momentum back on the Real Analysis playlist.
these videos are amazing i would wanna ask for some on cauchy criterion of series🙏🙏
Well explained for me
Awesome, thanks for watching!
Arigato :3
Why does the intersection have to be of a finite collection ?
take the set A_n= (-1/n,1/n), then the infinite intersection of all A_n such that n is a (non-zero) natural number is the set {0}. But there is no neighborhood of 0 such that this neighborhood is contained within the set {0}, so it is not open
@@sHexuality AH that makes so much sense, thanks a lot !
😩 ρɾσɱσʂɱ