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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 composition of continuous functions is continuous using the sequence definition of continuity. We assume g is a function from A to B, and f is a function from B to the reals. We assume g is continuous at c in A and f is continuous at g(c) in B. We can then apply the sequential definition of continuity to prove that any sequence in A converging to c has a sequence of images converging to f(g(c)). #realanalysis Definition of Continuity: https://youtu.be/O98eOlHyWmQ Basic Continuity Laws: https://youtu.be/Sbk-DDhuEvc Sequential Characterization of Continuity: https://youtu.be/AwC2S_dF8vg ★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