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 😁😁

You're such a humble teacher, I love it!

@michaelkoch6863

3 жыл бұрын

^^

Thank You For ALL You Do, you Are A Great Instructor

Great video, you make studying math truly fun and very helpful thank you

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

2 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

2 жыл бұрын

@@drpeyam Yes! It's Rieffel, exactly! Got your message!

Thank you!

Thank You! A very good Explantation! I have a Little math Channel in italian and I appreciate you a lot

Thank you for good videos

Grandiosa explicación

Thanks for such a great content with love from India

What of things with Cauchy ! Thank you very much for this demonstration Dr Peyam.

It's the second time that i see the video, i find it always hard but thank you very much.

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

You should make a video about field norms and Ostrowski’s theorem

Why is this so comfortable 🥰

Make some more video on metric space please

@drpeyam

3 жыл бұрын

See playlist

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?

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?

where is the million subscribers? You deserve way more.

@drpeyam

3 жыл бұрын

Awww thank you!!!!

Well well.....

how did they think of all this out of thin air when these theorems were being developed, when this field was new 💀

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.

What's difference between undefined and indeterminant.

@drpeyam

3 жыл бұрын

Indeterminate is for limits usually, like 0/0

Sir i love your voice tune😂😂😅😅👍🏻