I don't know if you're aware of the incredible impact you have on students by uploading videos to KZfaq, but I'm sincerely grateful. My professor is a math prodigy, but he cannot teach. You've been the only source of help I've gotten for my real analysis class.

Once a while, you come across an explanation so perfect, it makes you realise how easy the topic that you never really understood actually was. This is that video!

The word everybody is looking for is Intuition! You've shown your intuition, which helps us see WHY you're doing certain things, it clarifies your steps in achieving the desired goal and that's something that teachers fail to do. They teach as if we're inside their brains! Thank you!

this video was 100 times better than my professors lectures. You were able to explain this process in 10 minutes, whereas he has explained it for hours across multiple days and I never got it until now!!

You are very clear in all your steps. It makes it easy to understand! Thank you so much!!💜

Hey I finally understood Cauchy sequences after a few days. Im taking Real Analysis right now and its been tough but rewarding so far

This was a very well done and helpful video! Thank you for showing everything so thoroughly!

Thank you! Very helpful!. I’m going to watch more and if you make more I’ll keep on watching these. You make it so easy for me to understand! I love that feeling when things click and you just learned something new. That is a gift and I appreciate so much. Thank you!

Really nicely explained, I barely use english in my daily life, but I must say that was one of the most helpful explanations I've seen on how to prove a sequence is Cauchy.

Thank you so much this was helpful

Thank you so much for this!!! I’m a college student that was taking real analysis, complex analysis, and abstract algebra, with a writing intensive course. All those classes combined, was way too much for me. Especially since I work. The class I dropped was real analysis bc it was eating up most my time. I’m sad I wasn’t able to finish it this semester but hopefully next semester I’ll be able to take it with less of a workload. I’ll def be looking through your vids in preparation! Flawless teaching!

Thank you, KZfaq man, for your contribution to society.

Great video! You have no idea how much this helps!

WOWWWW!!!! THIS IS BEAUTIFUL! Thank you! ❤❤❤

This is really a clear explanation. New subscriber here. Keep it up.

BEST EXPLANATION. THANKS SIR

This was beautifully done. Thank you. I have subscribed :D

Thank you so much. I am a big fan of your work... salute!!!

Thanks a million! I have subscribed to your great channel! :)

Really Helpful in my math assignment. :-)

Just beautiful

Amazing video, thanks for this great content!!

Hey, thanks 💜

Very impactful.....thank you so much sir

thanks , really straightforward

Thanks for this, one question, is it valid to go further in the inequalities and write that 1/m^2 + 1/n^2

Thank you so much 🥺♥️♥️♥️♥️

Thanks for the video! Got a midterm tomorrow

thanks

Very nice video ! Thank you!

could you go over how you went from n^2> 2/ε -> 1/n^2 < ε/2 because I don't understand how your dividing form N^2 and 2/ε?

yes, this was indeed helpful :)

Thank you very much. Good video.

Good stuff

thanks dude

Thank you very much

thank u king

Why does this not work when I apply the triangle inequality early? | n^2/(n^+1) + -m^2/(m^2+1) | < or = | n^2/(n^+1) | + | -m^2/(m^2+1) | Then I would show that n^2/(n^2+1) is smaller than Epsilon/2 (and the right side respectively), however It seems impossible to show it this way. Is it just down to luck to get the correct reshaping done before applying it?

Thanks for the great video! I follow it all except for one step. How do you know e/2 is a suitable choice for each term? The requirement of |a_n - a_m| < e can be still be satisfied if one term is larger than e/2 as long as the other is less than the difference between 1 and the first term.

very easy thanks/

Nice video

Nice vedio, but how about 1/ sqrt(n(n+1)) which is diverges?

Thanks for the video. I'm not sure if I'm missing something, but why does N suddenly become larger than sqrt(eps/2) at the end when it was previously defined as N>sqrt(2/eps) at the start of the final part of the proof?

excellent. Just that auto write on the bottom of the video bothers me a lot. is there anything that can be done about it

Very nice video but you made a mistake on 11:01....... Well np ,still a wonderful video

🔥💋

so im the only one that didn't get it, nice!

why did not my professor show step by step

This is fucking algebra

thanks