Check out the Real Analysis Playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@nihilisticboi35203 жыл бұрын
The moment you finished explaining the 1/100 example, I felt I reached enlightenment. Beautifully explained!
@WrathofMath3 жыл бұрын
That's the best I can hope for! Thanks for watching, I am glad it helped!
@SequinBrain3 жыл бұрын
if only textbook authors knew the value of using numbers in math books...
@pxlbits64423 жыл бұрын
I learned more in this video than my entire semester in analysis class lmao...
@WrathofMath3 жыл бұрын
Well that's good and bad haha - I'm at least glad my video was helpful! If you're looking for more analysis, check out my analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Lots more analysis coming! And if you're in the mood for some tunes, check out my new math song that came out today! kzbin.info/www/bejne/ZoDVoGVujdCtmMk
@hamadkhan23393 жыл бұрын
Sir, this is the best lecture of this topic on u tube. Thank u so so much for explaining everything. This was hard to me but u explained it in a very easy way. why so underrated? You are really good, I hope that soon you will have subs in millions🙏🙌
@WrathofMath3 жыл бұрын
Thanks for watching, Hamad! I really appreciate your kind words! It's a very important topic so I'm very glad you found my explanation clear! The long road to a million awaits us!
@stephen34182 жыл бұрын
These intro to analysis videos are incredibly valuable. You have clarified the ‘setting out’ stage of the proof that my textbook simply failed to describe. How to choose an N? Thanks to your teachings, I can understand analysis and apply its techniques! I had thought that perhaps I had truly arrived at a level of maths which I’d find incomprehensible (at least without some miraculous discovery), but your teachings elucidated the simple technique of how to algebraically decide what N ought to be. So thank you so much! This will certainly be the most valuable lesson in analysis of my life! Such is the nature of this incredible inflection point!
@manarmagdy23297 ай бұрын
I cryied because I couldn't understand that and my exam after 4 days but now it's more than clear. Really thanks from my heart
@swastikadeb8605 Жыл бұрын
I was really struggling to understand the definition of limit clearly. I looked up everywhere on the internet until I found this video, such nicely explained with that amazing 1/100 example. It's totally clear now! Thank you sir. Hope this reaches to everyone out there.
@nikeshlilani52153 жыл бұрын
this is by far the best lecture on this topic on youtube..thanks a lot sir !
@WrathofMath3 жыл бұрын
That means a lot, thanks so much! I am glad it helped and let me know if you ever have any questions!
@bigollameo2 жыл бұрын
Now I finally understand what the "n>N" condition means. For the longest time I've been puzzled as to just what this relation requirement was trying to communicate. Should have been apparent years ago, but better late than never. Thank you!
@WrathofMath2 жыл бұрын
So glad it helped, thanks for watching!
@toxicfreeze-brawlstars12110 ай бұрын
bro i still dont understand this n>N can you explain
@toxicfreeze-brawlstars12110 ай бұрын
i mean what is the big n here
@blazobanicevic9 ай бұрын
@@toxicfreeze-brawlstars121 not sure if I got it myself but as for how I understand it, n is the index of an element of sequence (an) and N is a number so when you say n>N I think it is saying that every next element of a sequence after number N has to be between the limit and number N(so if I say 1/n and N=100 then every element after a100-after 100th element of a sequence-has to be between limit and 1/100 for every n>N) hopefully I helped but as I said I dont understand it completely however this is the way I currently understand it to be.
@nateman44ify3 жыл бұрын
My professor just went over this topic and I just could not follow along or understand what he was trying to say. But this actually makes sense, because of you im actually completing my homework. Thank you!
@WrathofMath3 жыл бұрын
So glad you found it helpful! Thanks for watching and let me know if you ever have any questions!
@bactran77992 жыл бұрын
amazing explanation of the limit of sequence definition that blows my mind. Thanks a lot Wrath. Please keep doing your great works
@WrathofMath2 жыл бұрын
You're very welcome, thanks so much for watching! If you're looking for more analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@IdoYos3 жыл бұрын
Best explanation I have found so far!! If you could make videos explaining linear algebra as well it would be phenomenal!! Thank you so much!!
@WrathofMath3 жыл бұрын
So glad to hear it, thanks for watching! You can find more analysis lessons in my Real Analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli As for linear algebra, I definitely plan on getting to it, but it will be some time. It was not one of my stronger subjects in college, so I have more than just brushing up to do!
@IdoYos3 жыл бұрын
@@WrathofMathHaha tell me about it 😉 Thanks again for a great intuitive explanation!!
@ConstanceShayamano-ei7fc11 ай бұрын
Yu the best online teacher I have ever encountered with
@liss352 жыл бұрын
perfectly explained, well defined that makes things clearer than on the mere printed definition from the book.. Thanks for this tutorial video it really helps a lot.. 👏👏👏
@WrathofMath2 жыл бұрын
So glad to hear that, thanks for watching! If you're looking for more analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@Anonymous-rv3gz3 жыл бұрын
Man you saved my 48hrs of stress...... May god bless you man.....
@WrathofMath3 жыл бұрын
So glad it helped. Thank you very much for watching!
@zb577511 ай бұрын
Your videos and your teaching skills are outstanding. Thank you for all your work.
@WrathofMath11 ай бұрын
Thank you!
@VocalBeast Жыл бұрын
Man thank you so much. Was pretty stumped understanding this but you explained it so clearly, thank you:)))
@WrathofMath Жыл бұрын
Glad to help! Check out my analysis playlist for more and let me know if you have any questions! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@existentialrap52110 ай бұрын
We makin it outta the trenches with this one. That visual helped a ton. Made the absolute value of an-L make sense.
@nuggeteater693 жыл бұрын
best video i have found for this so far
@WrathofMath3 жыл бұрын
Glad to hear it! Thanks for watching and if you're studying real analysis be sure to check out my analysis playlist, many more lessons to come! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@hanskywalker1246 Жыл бұрын
Finally somebody explained why we have to use N instead of just always n, thanks!
@WrathofMath Жыл бұрын
Glad to help, thanks for watching and let me know if you ever have any questions!
@hanskywalker12463 ай бұрын
@@WrathofMathI have a question: 9:31 can't we also say that |an-L| is greater zero because like the limit will actually never reach the final value?
@BlaqueT2 жыл бұрын
This video was a good step to help my understanding, as this epsilon definition of a limit has confuded me so much in the beginning of my real analysis course. Thank you so much!
@WrathofMath2 жыл бұрын
So glad it helped! Thanks for watching and check out my analysis playlist for more! Let me know if you have any questions! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@OGMarkuss Жыл бұрын
Hello Wrath of Math. I'm preparing for a test righ now. The explanation in masterly presented, although I don't understand there part where you wrote N > 1/e . Could you, please, briefly explain why is that so?
@fatimaintekhab735710 ай бұрын
Thank you for explaining the definition with a graph! I was really struggling with this❤
@aqsamaryam85803 жыл бұрын
I think it is the best explanation for anyone to understand this concept.....
@WrathofMath3 жыл бұрын
Thanks a lot, I'm very glad to hear that! 😊
@victoriacorcimaru1731 Жыл бұрын
Best, most intuitive explanation!!! A must watch )))
@WrathofMath Жыл бұрын
Thank you! Lots more analysis lessons to come - thanks for watching!
@marcusnzioka66243 жыл бұрын
thanks for this explanation, I have struggled looking for good content like this
@WrathofMath3 жыл бұрын
Thanks for watching, Marcus! If you're looking for more analysis, check out my Real Analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli And let me know if you ever have any video requests, lots more analysis lessons coming!
@chad2336 Жыл бұрын
best explanation so far, great video man!
@WrathofMath Жыл бұрын
Thanks Giga-Chad!
@snclassical82633 жыл бұрын
I hated Real Analysis and THANK YOU! for giving me new hope!!
@braverodger3 жыл бұрын
you explain very goodly. thank you!
@WrathofMath3 жыл бұрын
Glad it was clear, thanks for watching!
@dark.violin11 ай бұрын
You are really good at explaining. Thank you so much :)
@alfieplant69272 жыл бұрын
Perfect explanation. I understand completely now
@WrathofMath2 жыл бұрын
Glad to hear it! Thanks for watching, and check out my real analysis playlist if you're looking for more!
@mathechne10 ай бұрын
just the classical, very good, thanks
@evgenirusev8183 жыл бұрын
Super clear and intuitive. Thanks!
@WrathofMath3 жыл бұрын
So glad it was clear! Thanks for watching!
@Teja-tm4zi8 ай бұрын
excellent vid! thank you so much for the effort you put into these videos!
@WrathofMath8 ай бұрын
Thank you for watching!
@Carol.269 ай бұрын
Thank you so much Sir! Your explanation was really helpful!
@WrathofMath9 ай бұрын
Glad it helped!
@michelleyuangu746211 ай бұрын
So well explained. Thank you so much
@WrathofMath11 ай бұрын
Thanks for watching!
@deisooja2961 Жыл бұрын
this was an excellent video about limit of sequences. I was on a lecture and didnt understand shit about it. Really thanks man !!!
@WrathofMath Жыл бұрын
Glad to help!
@Naqvi-u8k11 күн бұрын
Thanks alot for your effort ❤❤😊😊
@successorof68 Жыл бұрын
I know the video is 3 years old but if you see this can you show an example where the definition for convergence of a sequence breaks. Maybe something like this: Prove 1/n limit is 1 when n goes to infinity. We know 1/n approaches 0 as n goes to infinity but would like to see how the proof breaks
@danielcamacho54343 жыл бұрын
amazing work dude! thank you so much!
@WrathofMath3 жыл бұрын
Thank you, it's my pleasure! Be sure to check out my Real Analysis playlist if you haven't, many more analysis lesson to come! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@rishabhsharma19822 жыл бұрын
Great video, incredibly helpful!
@J078_3 жыл бұрын
Gud work sir....keep updating with sch wondrfl classes from real analysis....
@WrathofMath3 жыл бұрын
Thank you! Will do, I have many more analysis lessons planned. Let me know if you have a specific request you'd like to see soon!
@user-kw9do1nx6l3 жыл бұрын
Thank you for making this clear! Could you maybe tell me how this example would work if we could guess the limit L of the sequence? How would we take out the absolute value, etc?
@citizenofreality2751 Жыл бұрын
WOW! Thanks for all the work!
@mahmoudalbahar16413 жыл бұрын
Many thanks for this good video.
@aniketgupta1340 Жыл бұрын
at 10:40 , i guess there is a mistake cuz for some a>b and a>c, we cant establish the fact that b>c or c>b
@pamodpeiris1542 жыл бұрын
Best explanation of limit..
@WrathofMath2 жыл бұрын
Thank you, glad it was clear! And if you're looking for more analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@hanskywalker12463 ай бұрын
I have a question: 9:31 can't we also say that |an-L| is greater zero because like the limit will actually never reach the final value?
@hilmakara4907 Жыл бұрын
May you please do another video with examples involving accumulation points
@aubreydebruyn844 ай бұрын
I consulted YT vids and RA books, did not get the N part. As so as you put on a graph, the lights turn on. Thank you so much.
@WrathofMath4 ай бұрын
Glad to help - thanks for watching!
@karlathebarla2 жыл бұрын
Excellent explanation!!
@WrathofMath2 жыл бұрын
Thanks Karla! If you're looking for more analysis, check out my playlist and let me know if you ever have any questions! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@sahelaria993 Жыл бұрын
Thanks that was very helpful
@WrathofMath Жыл бұрын
Awesome, thanks for watching! Lots more analysis videos on the way, let me know if you ever have any questions!
@sukhofruktt11 ай бұрын
you are a life saver!!! thank you so much
@IODell2 жыл бұрын
Great explanation. Thanks.
@WrathofMath2 жыл бұрын
My pleasure, thanks a lot for watching! If you're looking for more real analysis, check out my playlist! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@khalilmohammed22973 жыл бұрын
Thank you so much, you are brilliant
@zyshri10 ай бұрын
Thankyou so much sir 🌸✨❤️
@WrathofMath10 ай бұрын
Glad to help - thank you for watching!
@EduardoAdameSalles3 жыл бұрын
Thank you! BTW, what is this board software you use with the drawing tablet?
@WrathofMath3 жыл бұрын
You're very welcome, thanks for watching! I use Notability on iPad Pro! It works great! If you're looking for more real analysis, check out my Real Analysis playlist and let me know if you have any video requests! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@EduardoAdameSalles3 жыл бұрын
@@WrathofMath Thanks for answering. I'm actually having calc 1, but my professor have decided to start by Real Analysis. In fact, calculus isn't that hard, but I'm not sure about my skills in RA. I'll certainly be watching your videos
@mohamedbenjbara8663 Жыл бұрын
thank you for the approach 😍😍
@WrathofMath Жыл бұрын
Glad to help, let me know if you have any questions!
@ioannaathineos526910 ай бұрын
Master ! Thank you
@WrathofMath10 ай бұрын
Glad to help!
@mohamedaliekoroma50403 жыл бұрын
I enjoyed the lesson and I learned a lot. You don’t mind me sir; I have a question that I want you to help me solve.
@mauryaneha5893 жыл бұрын
This vedio very helpful for me. Thank u so much sir
@WrathofMath3 жыл бұрын
You're very welcome, thanks for watching!
@mauryaneha5893 жыл бұрын
@@WrathofMath sir plz upload some examples of limit of a sequence
@kehalitadesse51653 жыл бұрын
Thanks man that helped a lot
@WrathofMath3 жыл бұрын
So glad to hear it! Thanks for watching and if you're looking for more analysis, check out my real analysis playlist: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Many more on the way!
@azizahsaswandila67082 жыл бұрын
Thank you Sir
@WrathofMath2 жыл бұрын
Glad to help! Thanks for watching and check out my analysis playlist if you're looking for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@sukrandinc58362 жыл бұрын
Perfect, thank you
@WrathofMath2 жыл бұрын
Glad it was helpful! Let me know if you have any questions and check out my analysis playlist for more! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@EvrYRAp Жыл бұрын
holy. you are so good
@mohamedaliekoroma50403 жыл бұрын
This is my question; Sum the following series “the sum of n where r = 1 ~ r(r-1)
@cyrillamphosa32852 жыл бұрын
Great stuff
@jjjusb79735 ай бұрын
thank you
@WrathofMath5 ай бұрын
You're welcome!
@navyatayi69563 жыл бұрын
And why is epsilon any positive number close to 0? Why not a negative number?
@WrathofMath3 жыл бұрын
Let An represent an arbitrary term from a sequence which converges to L. Epsilon is positive because it is used to describe how the distance between a convergent sequence and its limit gets arbitrarily small. The distance between An and L is |An - L| which is always at least 0 by definition. Thus, it is arbitrarily small positive numbers which the distance between An and L must get less than, since by definition it will always be greater than any negative number. For a convergent sequence, |An - L| will eventually be smaller than any given positive number epsilon. Does that help?
@navyatayi69563 жыл бұрын
@@WrathofMath yes it does. Thank you very much. I understand now. Amazing video btw :)
@user-db2fo7of7e9 ай бұрын
what do you think about n=1+[1/e]
@syedalauddinbukhari98013 жыл бұрын
help a lot man thankx
@WrathofMath3 жыл бұрын
My pleasure, thanks for watching!
@WiskundeTraining2 жыл бұрын
what is the difference between the N-epsilon definition and the epsilon-delta definition? why we need to use the N-epsilon definition for a sequence and not the epsilon-delta one?
@WrathofMath2 жыл бұрын
Thanks for watching and good question! The N-epsilon definition is for limits of sequences as n goes to infinity. The epsilon-delta definition is for limits of functions at their accumulation points.
@guranahemanthkumar89763 жыл бұрын
Thank you So much :)
@WrathofMath3 жыл бұрын
My pleasure, thanks for watching! Be sure to check out the whole Real Analysis playlist if you haven't, many more new lessons to come! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli
@navyatayi69563 жыл бұрын
Here how is the value of epsilon considered? Is it a value related to the series or is it any number?
@WrathofMath3 жыл бұрын
Thanks for watching and epsilon is an arbitrary positive number. For any positive epsilon, a convergent sequence will eventually get within epsilon of its limit. Does that help?
@noahniklaus50703 жыл бұрын
Thank you
@WrathofMath3 жыл бұрын
No problem, thanks for watching! Looking forward to making some more real analysis lessons.
@Godfather-ps6zv Жыл бұрын
Man love from India
@WrathofMath Жыл бұрын
Love back from Cape Cod!
@Itsjustj82 Жыл бұрын
Why do we say that the bigger N is greater than 1/epsilon? (N>1/E)? please someone answer, i'm confused..
@hatemelsaudy88926 ай бұрын
Me too 😢
@user-xg8zi9tm7u10 ай бұрын
You are best
@WrathofMath10 ай бұрын
Thank you!
@ekemm3 жыл бұрын
Thanku, and i subscribed 😁😁
@WrathofMath3 жыл бұрын
My pleasure and thank you for watching and subscribing! Let me know if you ever have any requests!
@mo80463 жыл бұрын
What could go wrong if I tried to prove that the sequence converges to any other number? What could go wrong if I tried to prove that, for example, (n+1)/n converges to 3 rather than 1?
@WrathofMath3 жыл бұрын
Thanks for watching and that's a really great question! You should give it a go! Try proving (n+1)/n converges to 3 the same way you normally would. As you work with the expression | (n+1)/n - 3 |, you'll eventually see an expression clearly greater than or equal to 1 for all n, so you'll not be able to make it arbitrarily small. Then, you could say for epsilon = 1 and all n, we see what you just showed about | (n+1)/n - 3 | being at least 1, and so clearly there is no N that will make | (n+1)/n - 3 | less than epsilon for all n > N; proving the sequence does not converge to 3. I may make a video on this, it's a great thing to see when we begin working with the limit of a sequence definition!
@mo80463 жыл бұрын
@@WrathofMath Thanks for the great explanation!
@athethird49453 жыл бұрын
Aahhhhh thank you, When am Amat major attempts pmat
@realworld271610 ай бұрын
What is N?
@noorjahanjaleel81163 жыл бұрын
can you make vdios on properties of infinite series of real analysis
@WrathofMath3 жыл бұрын
Thanks for watching and I have more real analysis lessons in the works. If you have a request for a specific property of infinite series I can try to hurry that one along!
@sumeyye7014 Жыл бұрын
How can we assume that N is bigger than 1/Epsilon ?
@WrathofMath Жыл бұрын
N is a thing that we can choose, it effectively represents how far in the sequence we need to go in order to make the rest of the math work. When we do an epsilon proof, we're proving that no matter how small epsilon is, we CAN go far enough in the sequence so that all terms are within epsilon of the limit. N will generally depend on epsilon, because the smaller epsilon is, the further in the sequence we need to go in order to be sufficiently close to the limit.
@brainsofmathematics9992 жыл бұрын
I can't explain how much u help me
@tashfeenamahmud43913 жыл бұрын
but what if a_n
@WrathofMath3 жыл бұрын
Thanks for watching and good question! Yes, the definition works just the same. Remember we use the absolute value, we require that | a_n - L | is less than epsilon. This is the distance between a_n and L, and it does not matter whether a_n or L is negative. Their distance, given by | a_n - L |, will always be nonnegative.
@bernatbosch Жыл бұрын
2:16 "then, as like in this example, our sequence approaches zero, I can guarantee that..." and for me that is the problem of this type of definition of what a limit is: that just works if you already know in advance what the value of the limit is. Because otherwise, how could you calculate the absolute value of the difference between a number and L when you don't know yet what is the limit of the function as it approaches to...etc. A good definition of a limit L should be developed without having to know in advance the value of L. Otherwise, why the hell you need the definition if you are already sure that a certain number is indeed the limit you are searching for. Another idea that bothers me is that this particular way to prove seems just adapted for the case that we are wanting to know the limit of the sequence when it grows to infinity, but does not seem to be a good way to prove the limit of a sequence when it approaches a certain index n (lets say n=0 or n=1).
@WrathofMath Жыл бұрын
It should be unsurprising that to prove a limit converges to L, we need a candidate for L. There are various other ways this might take form, but regardless it is not like we have to KNOW what a limit is for sure before we can attempt this sort of proof, we need only a candidate, a number we think the limit is. With specific sequences, computation and/or intuition can produce a reliable candidate. In other situations of analysis that are less particular, a candidate may be rather abstract, and thus a proof of the convergence is very important. In our proofs of all the sequence limit laws, we don't KNOW the limit of a_n + b_n is a + b, but we suspect it is and so proceed with the proof to settle the matter. All that said, it is no doubt a significant and necessary weakness in this definition that you point out. The fact we must have some idea what the limit could be to use the definition is an obstacle. Later in my analysis playlist are several videos about Cauchy Sequences, in which we develop an equivalent definition of a convergent sequence that does not depend on the limit at all. Regarding the n to infinity point - there is no way, as we have defined sequences, to take a limit anywhere other than infinity. For any sequence a_n, if we consider the "limit as n approaches 4" for example, this doesn't really mean anything. The closest n gets to 4 is a_3 and a_5. In each case, either a_3 = a_4 and/or a_4 = a_5. Or, there is some distance between these terms. This is to say, a_4 either does not get approached by its neighboring terms, or it equals its neighboring terms. In a functional limit this is different because we could take a limit as x approaches 3 since x actually CAN approach 3. x = 2.9, 2.99, 2.999, etc. But for sequences, n is discrete, and can approach nothing other than infinity. Hope that's helpful!
@AUwalaSahaj3 жыл бұрын
Nyc sir
@WrathofMath3 жыл бұрын
Thank you!
@si_monster73653 жыл бұрын
10:39 Why does the big N have to be bigger than 1/epsilon?
@WrathofMath3 жыл бұрын
Thanks for watching and for the question! In the scratch work we did, we saw that n being greater than 1/epsilon will give us the result we want. However, by convention/definition, we don't take n to be greater than whatever we please, we only have that n is greater than N. I think of N as some point in the sequence, after which we get what we want. So since we want n to be greater than 1/epsilon, and we will have n > N, and we can pick what N is greater than, we need N to be greater than 1/epsilon so that n is as well. Then we're saying as long as we pick N to be greater than 1/epsilon, all terms of the sequence after the Nth term will satisfy our desired inequality. So for all n > N, |1/n - 0| < epsilon. Does that help?
@si_monster73653 жыл бұрын
@@WrathofMath Very clear, thanks!
@muhtedbaig7011 Жыл бұрын
@@WrathofMath thanks for the explanation I really appreciate it. I just had one query. Since n>N, we can also consider N to be *greater than or equal to* 1/epsilon right? Adding that *or equal to* shouldnt affect it as n>N. I would be glad ify help me clear this confusion :)
@rodrigodeboni410810 ай бұрын
YOU A G
@seriel59533 жыл бұрын
can N equals epsilon?
@sayakray47403 жыл бұрын
epsilon is a very small number close to zero. Whereas in the definition you need a number n such that n>N and the distance between f(n) and the limit should be less than epsilon. Now for us to get this value of limit we must increase this value N as much as possible so that we can go more closer to the value of the actual limit of the sequence. That is why N can't be equal to epsilon. You can always put them to be equal but then you won't be reaching any close to the limit.
@seriel59533 жыл бұрын
@@sayakray4740 thanks for replying, im confused because i found some youtbe videos that put them = instead of > ... but u cleared my doubts thanks a lot👍
@TheLudwigWan6 ай бұрын
Too bad you couldn't provide a counterexample...
@bernatbosch Жыл бұрын
From 10:32 to 11:52 the reasoning is unnecessary because at 10:32 it was demonstrated that any n greater than 1/epsilon would match to the inequality.
@WrathofMath Жыл бұрын
True, but the introduction of a definition like this is not the time for proceeding quickly in an explanation. I am deliberately redundant at times for important definitions.
@raulmarin15842 жыл бұрын
wonderful explanation..its very useful to me as a beginner teacher in real analysis. please give me instructions how to send donations in paypal im from the philippines
@mafongoyafrank40852 жыл бұрын
🔥
@WrathofMath2 жыл бұрын
Thanks for watching!
@0.O0x2 жыл бұрын
It is arbitrary guys...
@WrathofMath2 жыл бұрын
What's arbitrary? Certainly not this definition! But the positive epsilon, yes!
@amir_xtz92211 ай бұрын
❤❤❤❤
@user-wl9mw2oj9dАй бұрын
احتاج الشرح بالعربي
@MindMathMoney4 жыл бұрын
First! 😎
@WrathofMath4 жыл бұрын
Thank you for watching! 😎
@wafickhalife20333 жыл бұрын
you sound exactly like iDubbbz
@WrathofMath3 жыл бұрын
I've received several voice comparisons, but haven't seen that one! I can't say I hear the resemblance, but if you do some others probably do too. I remember sitting down in my old college apartment after class to watch the Content Cop on Ricegum, those were the days!