This is very helpful, but as a note I think it's more intuitive to explain the Archimedean property as : for any real number there is a natural number bigger than it and then use the corollary (there exist 1/n for all r>0 such that so and so) to prove love the good work
@brightsideofmaths
3 жыл бұрын
Yeah, this might be a matter taste for the Archimedean property. Thanks for the explanation there!
@chilledvibes99
3 жыл бұрын
yeah at uni we learn it this way :)
@IsomerSoma
3 жыл бұрын
I am watching your lectures as preparation for my 1st Semester. Thank you very much.
@PunmasterSTP
2 жыл бұрын
How'd your first semester turn out?
@ChrisSwaningAround
3 жыл бұрын
Great stuff You do a great job of filling in those gaps the modern education can leave in a mathematics education 😁 Keep it up!
@realAhmedAbdElGhany
2 жыл бұрын
i really like this channel, i really support this great effort i wish success for you in all the fields of your life !
@brightsideofmaths
2 жыл бұрын
Thank you so much 😀
@Negs42
2 жыл бұрын
@@brightsideofmaths Eine Anfrage bitte; Kannst du eine Serie über Differentialgeometrie machen? Danke
@leyashalabi7209
Жыл бұрын
الله عليك يا احمد
@dextreme1754
Жыл бұрын
Just started with this whole series I'm studying computer engineering and now I realised with your videos and explanation that Analysis is actually not that hard atleast on this level tho i had problems with even these simple concepts i guess it really depends on the teacher if the student can learn what they teach so I'm very grateful for you! Thank you!
@gianniskallionis3300
Жыл бұрын
as a greek, im proud of how u pronounce ε , good job !
@PunmasterSTP
2 жыл бұрын
Sequences and limits? More like “Surely this playlist contains only hits!” Thanks again for making and sharing so many high-quality videos.
@declandunleavy8985
2 жыл бұрын
Superb explanation as usual. You are a gifted communicator. One tiny piece of feedback - when watching videos on youtube there are many times when I want to pause the video to take in what is on the screen, like many other viewers I'm sure. This action always brings up the progress bar with its icons. If the text is written right to the very bottom of the screen it gets covered by the icons and can't be viewed on pause. Even after unpause it takes several seconds for the icons to disappear. An example occurs at the end of this video and I've noticed it on other vids too. Would be helpful in future vids if you left the bottom 5% of the screen blank. More an issue with youtube than your vids but unlikely they will change this anytime soon. Anyway - I hope you keep up the incredible work. Thanks!
@brightsideofmaths
2 жыл бұрын
Thank you very much! There is a really helpful feedback I also got before. I try to avoid writing at the bottom but sometimes I also want to show the stuff above at the same time and then I really want to use the whole screen. One possibility for you would be to use the pdf versions of the videos while watching the video. However, I try to be more careful in the next videos and try to avoid the bottom of the screen more often :)
@laviekolchinsky9441
3 жыл бұрын
Are you finished the series on constructing the basic number sets (R and C)? I've watched all the series you have except for these ones because I want to binge the full constructions and formalisms :)
@brightsideofmaths
3 жыл бұрын
Thank you! The construction of the real and the complex numbers is finished. However, I will add some videos about complex numbers soon but they are not need for the real analysis course here :)
@murilopalomosebilla2999
3 жыл бұрын
Beautiful presentation!
@pratikkumar311
3 жыл бұрын
Please upload more video on sequence and series.
@suryanarayanachebolu7870
3 жыл бұрын
Hats off for your good Job.
@vickysharma2949
2 жыл бұрын
Gefällt mir, wie du erklärst!😊. viel besser als Professoren an der Hochschule Baden Württemberg. Danke!
@chin6796
3 жыл бұрын
Thanks for uploading this series
@sadececansu9
11 ай бұрын
Waowww you 100% cleansed all my confusions Thanks Sir!!!!!!!
@brightsideofmaths
11 ай бұрын
Glad it helped! :) And thanks for the support!
@sadececansu9
4 ай бұрын
@@brightsideofmaths Hello Sir! I'm watching the video again after 7 months I realized everything is much more clear now than it was 7 months ago. I have a question can we simply choose N=1/ε instead of showing for Archimedean property
@brightsideofmaths
4 ай бұрын
@@sadececansu9 The Archimedean property is given and we have to use it :)
@sadececansu9
4 ай бұрын
@@brightsideofmaths Thanks for your reply : ] I follow another channel, too. And the teacher always do scratch work first to find delta (or N) then he chooses delta based on the scratch work. I haven't seen that he applies Archimedean Property- he just lets. He does this during the limits Epsilon- Delta proofs or N-delta M-delta proofs (for infinity).. Could you please tell me the reason why he lets Delta \ N
@glennlehman9608
Жыл бұрын
I like the pace and content of your videos. Personally, I find them easier to follow than my text, so I appreciate the effort you put into the explanations. At the end of the video, you mention the Achimediam Property - I am not familiar with this. Do you have a video that explains the property?
@brightsideofmaths
Жыл бұрын
Yes, you can find it here: tbsom.de/s/slm My Start Learning Mathematics series covers the construction of the real numbers. You don't need all the videos for understanding the Archimedian property. And thanks for liking me videos :)
@glennlehman9608
Жыл бұрын
@@brightsideofmaths I think I might need all the videos ... Thanks Construction of the real numbers has been confusing me
@kamildiril9544
5 ай бұрын
Thank you very much for an excellent explanation. I didn't understand the logic epsilon et N for 2 years. I understand them now.
@brightsideofmaths
5 ай бұрын
You are welcome!
@dawardeka5404
Жыл бұрын
lots of Love from IIT Bombay
@pratikkumar311
3 жыл бұрын
Thanks
@DrPeterkuah
6 ай бұрын
That is the best convergent definition I have ever seen /read.
@brightsideofmaths
6 ай бұрын
Nice! And thanks for your support :)
@shaunsankar5397
8 ай бұрын
You're a great teacher, props!
@ThwinMinHtet-q1s
Жыл бұрын
Thank u❤ You’re Genius sir.
@bArda26
2 жыл бұрын
Wow amazing and thank you for making these videos !
@gopinathan2095
3 жыл бұрын
Great insight I got...
@hz6612
9 ай бұрын
Thank you so so so much !!!
@shalvagang951
2 жыл бұрын
hey you told that you will make a lecture series on algebraic geometry or differntial geometry so when you are making it
@brightsideofmaths
2 жыл бұрын
I try to do this on this year :)
@brockobama257
2 жыл бұрын
I think I might pass real analysis
@inthebackwiththerabbish
2 жыл бұрын
You are amazing Dankeschön
@maxpercer7119
2 жыл бұрын
Fun challenge, negate formally the definition of convergence. For a bigger fun challenge, show that the sequence {-1, 1, -1, +1, ... } , given by the rule (-1)^n, does not converge. (Hint, it is not enough to show that the sequence does not converge to a specific number , e.g. 1 or -1, but we must show that it does not converge to any real number)
@shalvagang951
2 жыл бұрын
hey can you also do a video on algebraic geometry and differential geometry
@brightsideofmaths
2 жыл бұрын
Yes, I can :)
@shalvagang951
2 жыл бұрын
@@brightsideofmaths so when you are planning to do that because I am very excited
@peki_ooooooo
Жыл бұрын
Good explanation.
@brightsideofmaths
Жыл бұрын
Glad you think so!
@sivaramd5637
Жыл бұрын
So, a finite sequence never converges to any number "a"? Since, we can always choose 0 < epsilon < |a_n - a|.
@brightsideofmaths
Жыл бұрын
A finite sequence is just a tupel and convergence makes not much sense there.
@sivaramd5637
Жыл бұрын
@@brightsideofmaths Oh, okay. So, a sequence is infinite by definition (in real analysis)?
@vale_gamer5228
7 ай бұрын
Hello. I love the videos. Helping me a lot. Tho i still have a questions. Namely, what exactly is N(Not the N of natural numbers but just the capital N)? What does it represent???
@brightsideofmaths
7 ай бұрын
Thanks! N represents a natural number, an index. So N could have the value 5, for example.
@ИванМихайлов-ъ9п
Жыл бұрын
I have a question. Why is 1 to the power of infinty indetermined?
@brightsideofmaths
Жыл бұрын
Infinity is not a well-defined number for powers.
@dodysumargo
4 ай бұрын
Does a limit pf a sequence mean the largest value that sequence has?
@waraamir1487
3 ай бұрын
No for example if we take (-1)'n/n
@abdeljebbarmnahaj7641
9 ай бұрын
Great job
@chunyunyang8999
2 жыл бұрын
Hello, I am a student from mainland China, because of various reasons I can't pay, can you give me a PDF and channels to get your course
@leochen4584
Жыл бұрын
at 10.28 why is it not 1/n >=1/N cos like it said n>=N
@brightsideofmaths
Жыл бұрын
1/2 is bigger than 1/3 but 3 is bigger than 2.
@cprt.d9471
Жыл бұрын
Wie nennt man die neighbourhood auf Deutsch? Wird es in der Mathematik ebenso mit Nachbarschaft übersetzt? :'D Und wie wird der archimedian properity übersetzt?
@brightsideofmaths
Жыл бұрын
Neighbourhoood = Umgebung :)
@dodysumargo
4 ай бұрын
Does a limit of a sequence mean the largest value the sequence can give?
@brightsideofmaths
4 ай бұрын
No!
@dodysumargo
4 ай бұрын
@@brightsideofmaths alright then, so what does it mean exactly?
@brightsideofmaths
4 ай бұрын
@@dodysumargo The value the sequence approaches for n to infinity.
@dodysumargo
4 ай бұрын
@@brightsideofmaths Oh, alright then thanks for the info, im new to real analysis
@brightsideofmaths
4 ай бұрын
@@dodysumargo You are welcome! You can join the community forum to discuss more problems :)
@intuitivelyrigorous
4 ай бұрын
Why |an-a| less than epsilon cant be |an-a| less than or equal to epsilon? Or it can be but both definition will prove the same convergence.(As there is always a number between two numbers so we will always have some other epsilon if not the epsilon which generates the case of equal to). Then is there any significance of choosing less than rather than less than equal to. If it cant then the case of equal to must be redundant, if so then how or the expression with equal to must not give proper idea of convergence.
@brightsideofmaths
4 ай бұрын
< eps and ≤ eps give the same definition.
@ra1n0
Жыл бұрын
8:09 shouldn't the definition of convergence state that |an - a| with the latter a being the limit you picked (the red a)?
@brightsideofmaths
Жыл бұрын
Yes, it should be a red a :)
@Marryatau
23 күн бұрын
Thank you for The sequence of videos well made lectures though On the example at 3:45 when defining the set of Natural Numbers, they’re both marked as a: so the starting index isn’t defined with the notation (an)n€N as the set N is ambiguous, because When the set of natural numbers begins at 1 then (-1)^1 is -1 as you have graphed while when the set of natural numbers begins at 0, then (-1)^0 is 1 and so the function’s range is corresponding to the index of N and the interesting question becomes whether they’re considered equal because essentially they’re both defining a sequence of alternating 1 units. Like the state of a transistor with their magnetic poles being + or - of course by set comparisons they’re two representations of the set of natural numbers (0,1,…) and (1,2,…) but essentially they’re both defining a state of (…-1,1,-1,1,…) so the starting index does correspond to the initial index of the mapping and they do define a set of two functions each with a differing starting index be it N0 or N1therefore I think n€N is ambiguous without a subscript on the N, there’s a great discussion on Stackexchange about this Natural Number indexing and I think It’s good to mention
@brightsideofmaths
23 күн бұрын
The set N is defined in the first minute of the video, compared to the set N0.
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