I don't know if you're aware of the incredible impact you have on students by uploading videos to RU-vid, 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!!
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!
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!
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.
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.
Hey, I'm no expert but I was watching an earlier video of his and the reason he picks e/2 is because you want the whole sum of 1/m^2 + 1/n^2 to be less than epsilon so if you can prove that each individual part(1/m^2 by itself) is less than e/2 then you satisfy this.
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?
