2 - Sequences in metric spaces

This video serves as an introduction to sequences in metric spaces, including convergence, divergence, Cauchy sequences, and how these compare to how things went for sequences of real numbers. It follows the sixth page of my course handouts, corresponding to the latter part of Chapter 3 in Carothers.
This video moves quickly! Please rewind, rewatch, and/or slow the playback speed as necessary---once the whole thing makes sense in real time, you're in pretty good shape with the basic concepts!

[@danielfrank2472]

By far the best real analysis video I've seen on the internet. Haha wishing you were my professor at the moment!

[@frankswenton3177]

Thanks! Glad these are helpful!

[@volkandemir6353]

Excellent! I checked the whole playlist but there were only 4 videos. Thanks for your effort!

[@Sky_osonoupo]

I really have no words. awesome explanation for something so arbitrary and complex, soon new mathematicians will be thanking you for it

[@frankswenton3177]

Thank you for the kind words!

[@Sky_osonoupo]

keep going with the hard work ! one question plz , which software do you use for animation ?

[@frankswenton3177]

@@Sky_osonoupo The text is brought in from LaTeX, and the raw static images that everything's based on are drawn in Illustrator---then it all gets put together in Adobe After Effects (with the audio) to make the videos. It's a bit of a pain, but I figure the result more or less lasts forever!

[@visualgebra]

Wow outstanding conceptual approach ❤ from 🇮🇳🎙👍

[@frankswenton3177]

Thanks! As a topologist, this is how I see all of this stuff. :)

[@Bbaobabb]

THANK YOU SO MUCH

[@frankswenton3177]

You're welcome!

[@the_informative_edge]

Nice lecture

[@Eis461]

Helpful