Please Subscribe here, thank you!!! goo.gl/JQ8Nys How to Prove a Sequence is a Cauchy Sequence Advanced Calculus Proof with {n^2/(n^2 + 1)}
Пікірлер: 82
@amaliacoughlan70714 жыл бұрын
I don't know if you're aware of the incredible impact you have on students by uploading videos to KZbin, 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.
@TheMathSorcerer4 жыл бұрын
Thank you!!
@imonsanyal2 жыл бұрын
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!
@kumailkhaki2664 жыл бұрын
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!
@TheMathSorcerer4 жыл бұрын
You are welcome!
@gisellabradley72705 жыл бұрын
You are very clear in all your steps. It makes it easy to understand! Thank you so much!!💜
@TheMathSorcerer5 жыл бұрын
no problem:)
@adriana_irl2 жыл бұрын
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!!
@sarahrickel84885 жыл бұрын
This was a very well done and helpful video! Thank you for showing everything so thoroughly!
@TheMathSorcerer5 жыл бұрын
thank you! so happy it helped someone!!
@InfinityMW22 жыл бұрын
Hey I finally understood Cauchy sequences after a few days. Im taking Real Analysis right now and its been tough but rewarding so far
@tonyreyes81904 жыл бұрын
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!
@TheMathSorcerer4 жыл бұрын
Yes I love that feeling too! Yes soon I will be posting more proofs❤️
@jonathanmolina76904 жыл бұрын
Great video! You have no idea how much this helps!
@TheMathSorcerer4 жыл бұрын
awesome!
@mptapasdas4 жыл бұрын
BEST EXPLANATION. THANKS SIR
@TheMathSorcerer4 жыл бұрын
thank you!
@Karim-nq1be Жыл бұрын
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.
@sourceOfJoy215 жыл бұрын
Thank you so much this was helpful
@frankie80862 жыл бұрын
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!
@TheMathSorcerer2 жыл бұрын
:)
@Fortune_Crown7 ай бұрын
WOWWWW!!!! THIS IS BEAUTIFUL! Thank you! ❤❤❤
@Sipnayan5 жыл бұрын
This is really a clear explanation. New subscriber here. Keep it up.
@TheMathSorcerer5 жыл бұрын
Thanks 😄
@taronmamyan49723 жыл бұрын
Thank you, KZbin man, for your contribution to society.
@vdav174 жыл бұрын
Thanks for this, one question, is it valid to go further in the inequalities and write that 1/m^2 + 1/n^2
@TheMathSorcerer4 жыл бұрын
Yes, that is much better, much cleaner! I like your way:)
@thembanovela42734 жыл бұрын
Thank you so much. I am a big fan of your work... salute!!!
@TheMathSorcerer4 жыл бұрын
You are welcome!
@d00b495 жыл бұрын
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.
@fabioutrilla71094 жыл бұрын
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.
@elizabethnziokikatunge20112 жыл бұрын
thanks dude
@zacharychild29934 жыл бұрын
Thanks for the video! Got a midterm tomorrow
@TheMathSorcerer4 жыл бұрын
good luck!
@ЕвгенияГанжа3 жыл бұрын
Thanks a million! I have subscribed to your great channel! :)
@vijaysinghchauhan7079 Жыл бұрын
Just beautiful
@graceododo94812 жыл бұрын
Very impactful.....thank you so much sir
@lemyul5 жыл бұрын
thanks
@sonic5d4 жыл бұрын
This was beautifully done. Thank you. I have subscribed :D
@TheMathSorcerer4 жыл бұрын
Awesome, thank you!
@diyagoyal66853 жыл бұрын
Really Helpful in my math assignment. :-)
@burakergocmen56614 жыл бұрын
thanks , really straightforward
@TheMathSorcerer4 жыл бұрын
glad it helped:)
@peterschannel20554 жыл бұрын
Thank you very much. Good video.
@TheMathSorcerer4 жыл бұрын
you are welcome:)
@dmitarzvonimirmitev66444 жыл бұрын
Very nice video ! Thank you!
@TheMathSorcerer4 жыл бұрын
you are very welcome!!
@elijah62184 жыл бұрын
Amazing video, thanks for this great content!!
@TheMathSorcerer4 жыл бұрын
you are welcome!
@Modi_M44 жыл бұрын
Thank you so much 🥺♥️♥️♥️♥️
@TheMathSorcerer4 жыл бұрын
glad it helped!!!
@kaizoku4life3 жыл бұрын
Thank you very much
@TheMathSorcerer3 жыл бұрын
👍
@pablolemus29833 жыл бұрын
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?
@mijajchokker1459 Жыл бұрын
Hey, thanks 💜
@tjk42612 жыл бұрын
yes, this was indeed helpful :)
@asmakhalid23564 жыл бұрын
excellent. Just that auto write on the bottom of the video bothers me a lot. is there anything that can be done about it
@TheMathSorcerer4 жыл бұрын
thank you:)
@nopewtfisthis7 ай бұрын
Good stuff
@greenrain553 жыл бұрын
thank u king
@TheMathSorcerer3 жыл бұрын
you are welcome:)
@scp_in_iitb29 күн бұрын
Nice!!
@annixu92193 жыл бұрын
Nice vedio, but how about 1/ sqrt(n(n+1)) which is diverges?
@slickmello73243 жыл бұрын
Nice video
@TheMathSorcerer3 жыл бұрын
Thank you
@peterschannel20554 жыл бұрын
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?
@TheMathSorcerer4 жыл бұрын
yeah you have to force it to work, you can always do things that won't work, the trick is, to make it work, that is the challenge!
@BlaqueT4 жыл бұрын
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?
@TheMathSorcerer4 жыл бұрын
I don't see it sorry! I looked I can't find what you are referencing:)
@BlaqueT4 жыл бұрын
@@TheMathSorcerer at the start of the proof (following the scratchwork), you defined N>sqrt(2/eps), but then at the end, it became N>sqrt(eps/2)?
@TheMathSorcerer4 жыл бұрын
@@BlaqueT I still don't see it sorry lol, where at the end?
@BlaqueT4 жыл бұрын
@@TheMathSorcerer I'll just grab the timestamp :)
@TheMathSorcerer4 жыл бұрын
@@BlaqueT I see it,small mistake thank you!!!
@ayanceferzade88823 жыл бұрын
very easy thanks/
@rishesmishra17405 жыл бұрын
Very nice video but you made a mistake on 11:01....... Well np ,still a wonderful video