Analysis 1 - Convergent Subsequences: Oxford Mathematics 1st Year Student Lecture

This is the third lecture we're making available from Vicky Neale's Analysis 1 course for First Year Oxford Mathematics Students. Vicky writes:

Does every sequence have a convergent subsequence? Definitely no, for example 1, 2, 3, 4, 5, 6, ... has no convergent subsequence. Does every bounded sequence have a convergent subsequence? Watch this video to find out!

You can watch many other student lectures including the other two lectures from this course via our main Student Lectures playlist (also check out specific student lectures playlists):

All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.

[andrewharrison]

It's great how much you can throw away from an infinite sequence and still have an infinite sequence. Then for complex numbers you do it twice!
Haven't looked at this sort of maths for about 50 years - great fun, enjoyed.

[harsh]

Thank you very much madam. Since your last video I was eagerly waiting for next video, Please upload the whole course.

[roygreen]

Hey, im writing here because i have an advice to give. I think you should make another video which shows the use of sets in some proofs. Even though you learn it more precisely in 3th year. For exampe, in calculus, almost all the lemmas in vicky videos starting with very specific type of sets and im sure that students can find it very difficult when and how to use them with very general definition. Im student too but what i can offer is:
1.to mention some sets with no repeated elements
2.Mention how to build set of functions compared to set of sequences, im sure this is huge difference and helps the idea of their differences
3. Infinite and finite sets and their properties, by scenic viewpoints lemma it seems that only infinite elements can tells monotone.

I know this information took me long time to understand by my own so i feel pretty bad that no one teach me those.

[miro.s]

Please make available also other additional supportive materials and those from Canvas

[anonimogarcia]

Good video! It would be lovely if those exercises you propose at the end of the video were put in writing. I mean, you enounce them too fast for my rusty mind!!

[alexitoyt]

*"I AM TOTALLY SURE THAT THE PERSON WHO STOPPED TO READ THIS MESSAGE WILL BE SUCCESSFUL IN EVERYTHING HE DOES"* 🥺

[masternobody]

First but I cant understand your hand writing rip