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Curated by: Anna1.618 (104 videos)
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 🛍 Check out my math clothing store: 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 We prove the limit law for the sum of convergent sequences. If a_n converges to a and b_n converges to b, then the sequence a_n + b_n converges to a + b. As in, the sum of convergent sequences converges to the sum of their limits. This is a fairly straightforward proof using the epsilon definition of a convergent sequence. Limit Law for Difference of Convergent Sequences: https://youtu.be/ZlAT0_W4yP0 Limit Law for Constant Times a Convergent Sequence: https://youtu.be/W3EWjNSoxqE Limit Law for Product of Convergent Sequences: https://youtu.be/Zvy860EOlVk Limit Law for Quotient of Convergent Sequences: https://youtu.be/wBNKbQ-xNiw Proving All the Sequence Limit Laws: https://youtu.be/dWLhfYUb3wc 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: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu