This is a beautiful theorem and a nice proof. Well done. It fascinates me that this construction relies on ℝ being a complete metric space. The completeness of ℝ seems to allow to construct a completion for every other metric space.
@drpeyam
3 жыл бұрын
Wow you’re right, I didn’t notice that
@harambesson1098
3 жыл бұрын
Exactly my thoughts. Thanks for expressing it more clearly 😁😁
@murielfang755
3 жыл бұрын
I am a visiting undergraduate to Berkeley and going to take Introduction to Topology and Analysis this semester. It is indeed a challenging course, and fortunately I see your videos. They really helpa lot! Thank you!
@drpeyam
3 жыл бұрын
Yay 202A!!! Isn’t Rieffel teaching it? I had him for 202B in Spring 2008. His class is tough but his homework is interesting! Tell him hi whenever you can 😁
@murielfang755
3 жыл бұрын
@@drpeyam Yes! It's Rieffel, exactly! Got your message!
@ashleyveliath4571
15 күн бұрын
Dr.Peyam, beautiful lectures. If you could put the camera at an angle that the board is not covered while you are writing (or some equivalent arrangement), I think it would be much easier for us to follow the lecture.
@umerfarooq4831
3 жыл бұрын
Great video, you make studying math truly fun and very helpful thank you
@trtlphnx
3 жыл бұрын
Thank You For ALL You Do, you Are A Great Instructor
@riadsouissi
3 жыл бұрын
Excellent video. At 20:00, to be more precise, shouldn't N(underscore) depend on k, so N(k)? In which case P* = [P(k, n+N(k)]? Also, at 22:00, I suppose [q(n)] is constructed from P* not P?
@matematicasemplice
3 жыл бұрын
Thank You! A very good Explantation! I have a Little math Channel in italian and I appreciate you a lot
@dgrandlapinblanc
3 жыл бұрын
What of things with Cauchy ! Thank you very much for this demonstration Dr Peyam.
@shivaudaiyar2556
3 жыл бұрын
Thanks for such a great content with love from India
@Nick-kg7sk
3 жыл бұрын
You should make a video about field norms and Ostrowski’s theorem
@thedoublehelix5661
3 жыл бұрын
The idea is really simple, but some portions of the proof are quite tricky !
@greatstuff5
3 жыл бұрын
So true
@greatstuff5
3 жыл бұрын
Bruh how ur comment a week earlier than the goddamn video itself
@thedoublehelix5661
3 жыл бұрын
@@greatstuff5 He has a playlist with all the videos from his analysis class in advance
@greatstuff5
3 жыл бұрын
@@thedoublehelix5661 ahhhhh lol I was like wth
@thedoublehelix5661
3 жыл бұрын
@Jose Ignacio Millán nope
@dgrandlapinblanc
2 жыл бұрын
It's the second time that i see the video, i find it always hard but thank you very much.
@mathssolverpoint6059
3 жыл бұрын
Make some more video on metric space please
@drpeyam
3 жыл бұрын
See playlist
@nicolascamargo8339
10 ай бұрын
Grandiosa explicación
@dushyanthabandarapalipana5492
3 жыл бұрын
Thank you!
@IzenaiYT
3 жыл бұрын
Why is this so comfortable 🥰
@kruksog
3 жыл бұрын
Ugh, I never took an analysis course, and I feel like it's such a big chunk missing from my toolkit. (If you're wondering why I missed analysis, I was getting a CS major as well and so took a ton of discrete math courses.)
@drpeyam
3 жыл бұрын
Check out the playlist, it will help
@kruksog
3 жыл бұрын
@@drpeyam Dr pi*m, you are such a quality instructor. Thank you for your suggestion. I will be sure to consider and explore it.
@francaisdeuxbaguetteiii7316
3 жыл бұрын
where is the million subscribers? You deserve way more.
@drpeyam
3 жыл бұрын
Awww thank you!!!!
@godthinkun
3 жыл бұрын
Thank you for good videos
@rikhalder5708
3 жыл бұрын
What's difference between undefined and indeterminant.
@drpeyam
3 жыл бұрын
Indeterminate is for limits usually, like 0/0
@ChuckNorris-ly6uo
3 жыл бұрын
how do you map a cauchy seq in S that say tends to sqrt(2) to S´? Is that seq considered a point in S?
@rikhalder5708
3 жыл бұрын
Well well.....
@ar3568row
8 ай бұрын
how did they think of all this out of thin air when these theorems were being developed, when this field was new 💀
Пікірлер: 40