NOTE: Around 08:58 when we discuss the closure of a set, I must clarify that the closure of A being a closed set is not as trivial as I made it sound. Certainly the closure of A contains the limit points of A, but when unioning A with L, it is possible we introduced NEW limit points of the set L, and thus to show the closure of A is closed, we'd need to consider this possibility. As it turns out, new limit points will not be introduced in this process, so closures are indeed closed, but again - it's not as trivial as I made it sound.
Bit late on this (I am just starting Uni), but these are amazing and so much better than lectures. You are doing God's work my friend. Keep pumping more high level math videos. I will watch all of them.
NOTE: Around 08:58 when we discuss the closure of a set, I must clarify that the closure of A being a closed set is not as trivial as I made it sound. Certainly the closure of A contains the limit points of A, but when unioning A with L, it is possible we introduced NEW limit points of the set L, and thus to show the closure of A is closed, we'd need to consider this possibility. As it turns out, new limit points will not be introduced in this process, so closures are indeed closed, but again - it's not as trivial as I made it sound.
Bit late on this (I am just starting Uni), but these are amazing and so much better than lectures. You are doing God's work my friend. Keep pumping more high level math videos. I will watch all of them.
Your lectures have definitely helped me a lot in these proofs in discrete maths
Glad to hear it! Thanks for watching and let me know if you have any video requests!
5:31 I like that you connected your discussion here with closure under an operation.
Legend man, legend man
Appreciate ya
Saving lives...
I'm doing my best! Let me know if you have any questions or video requests!
Will it be possible to create lectures on Topology in Real Numbers with n dimensions😣. @@WrathofMath
Thank you. it was great❤🔥
Glad to help - thanks for watching!