such a well-made video thanks a lot!

Thank you for video. Is closure one of the axioms?

Perfect and clear thank you madam

THANK YOU!

i want a vid shows that the set of all integers doesn't satisfy the completness axiom i need acounter example

I love this channel,sooo much Thanks ma for the precise Lecture

Thank you for the video! There're not so many youtube videos that provide such formal, organized proofs. I also think that it would be a good idea if you can upload videos about topology; this topic has very naunced details in its proofs, and I think your vidoes would be a very helpful source for students on that topic.

Thanks for this video🥰

Thank you

the sup of a set is the best upper bound

Thanks for all the course! What's the difference between range and codomain?

Amazing! *leaving comments for more views*

Thanks for the explanation. These seems to be very basical things such tht is hard to found it thoroughly explained like you did. It was very helpful. Greetings from Mexico

Hi, how come statement (2) at the end of the video is only a subset and not equivalent? I am struggling to see why you cannot apply the same logic that is used to prove (1) with (2) to get equivalence for (2).

Big thanks to you, my concept of preimages is crystal clear now! :) Very well illustrated with examples. 🙏

Nice video. Please make a video explaining convergent and divergent sequences.

अति सुन्दर

Delta should be the length of the cylinder. Calling this height makes the picture very confusing. The cylinder axis is aligned with x, which is hard to see.

show that A is a bounded set A{6n²/7n²+16 : n£N} Please help me and solve this. Thank you

Thanks a lot ur videos are amazing

𝔭𝔯𝔬𝔪𝔬𝔰𝔪 😭

Thank you for another excellent lecture. I appreciate all the effort that went into making this video.

Thank you for this excellent lecture. Just wondering if you have one that explains subsequences and the Bolzano-Weierstrass theorem and the epsilon neighbourhood of a.

Thank you for taking the time to make all these lectures available. Much appreciated.

thank you. beautifully composed maths and very understandable divided steps.

Amazing explanations. I am studying Real Analysis at the moment and I use your videos as supplement to the reading and lectures. I hope you will continue with your explanation videos :)

Very concise, I was able to follow along

I dont get how it can be 2 when if we come back to the beginning question it says r^2<2 and we say that it is 2 but 2^2 = 4 which is not less than 2... ?

I like the way you take your time to go through each step. Good one there😊

Please do some real analysis video for sequences

Thank u for the straight forward and easily followed explanation

I love your videos so much. Thanks for making me enjoy discrete maths.

Ma'am...what are the supremum and infimum of (0,1) intersection {m+n√2 : m,n are integers}?

The thing that confuses me about Supremum and infimum is that in sets that don't include the number such as (-infinity, 2) then 2 is the supremum. But 2 isn't part of the set. Does this mean that supremum and infimum are like limits in that you just get as tightly bounded to the set as you can from either side?

Thank you so much.

Solid material! Hope you could also cover little O and corresponding O notation in probability. Thx!

😉 P r o m o s m!!

very helpful, thank u sm ^-^

Hello ma'am! Your video is nice and well explanatory. Please kindly drop the link to the part 1

Great job, Big Epsilon! I'm a Russian teacher of math who worked for 20 years at the technical university. I wish I can speak English so fine... Despite of my natural hearing disabilities, I can hear every word you say clearly. Your voice is beautiful. The examples you eplained aren't complicated, but the way you are teaching is brilliant. Waiting for more videos from you. Thanks a lot!

Thank you so much excellent explanation

great one helped me a lot thanks ! can you give me a book name please that contain this topics

hey thanks so much that was very helpful but can you please recommend me a calculus book that contains this topics?

Dear madam, I don't usually leave comments! Your teaching is awesome , the way you approach theorems are lovely. This concept was eating my brain for few months, you literary saved me. Please don't stop uploading videos just because you don't get views! You are undoubtable one of the best teachers I've ever seen!! Love you madam!! Keep up the good work!! From Sri Lanka

Please make more videos on Analysis, I would love to see more analogies like the cylinder that can help me imagine or visualize the theorems or definitions.

That was an interesting way to think about uniform continuity. Thank you for making this video!

Excellent explanation ☺️

Thaanks

This was so helpful, Thanks!