Theorem 1: A monotone sequence of real numbers having a divergent subsequence is properly divergent.
In this video on Epselon++, we delve into an essential theorem in real analysis:
Theorem 1: A monotone sequence of real numbers having a divergent subsequence is properly divergent.
We provide a comprehensive explanation of this theorem, breaking it down step-by-step to ensure a clear understanding of its statement and implications. This theorem plays a crucial role in understanding the behavior of sequences in mathematical analysis, making it highly relevant for students and researchers.
This video will be especially useful for students pursuing BSc Mathematics or MSc Mathematics, as well as those preparing for competitive exams like CSIR NET, GATE, IIT JAM, TIFR, and other similar examinations. Mastering this theorem will enhance your conceptual clarity and problem-solving skills in sequence-related topics.
Timestamps:-
0:00 – Introduction to the theorem and its importance
1:10 – Definitions of monotone sequences and divergent subsequences
2:30 – Statement of the theorem
3:15 – Step-by-step explanation of the theorem’s proof
5:00 – Examples to illustrate the theorem
5:45 – Summary and key takeaways
#mscmaths
#bscmaths
#csirnetmaths
#iitjam
Chapter 5 Real Sequence
Link of Lecture 1 :- https://youtu.be/TaRTAVTvrMU
Link of Lecture 2 :- https://youtu.be/nq-Pa-lrWWM
Link of Lecture 3 :- https://youtu.be/8g0HX7W6eLo
Link of Lecture 4 :- https://youtu.be/B9phcAf3cgk
Link of Lecture 5 :- https://youtu.be/gcV7VFctaD8
Link of Lecture 6 :- https://youtu.be/vI7biPhry18
Link of Lecture 7 :- https://youtu.be/mFBYP7NjJOs
Link of Lecture 8 :- https://youtu.be/4RcxgM-WIVI
Link of Lecture 9 :- https://youtu.be/IaRr91cAp4g
Link of Lecture 10 :-https://youtu.be/INAgmY4phJg
Link of Lecture 11 :-https://youtu.be/m3eHHEM6nTw
Link of Lecture 12 :-https://youtu.be/AOx6OJKvTB0
Link of Lecture 13 :-https://youtu.be/oexcSOxxM9c
Link of Lecture 14 :-https://youtu.be/Oyi75_7BBZY
Link of Lecture 15 :-https://youtu.be/kzzEyNGqceE
Link of Lecture 16 :-https://youtu.be/Ly2rNBnd3aw
Link of Lecture 17 :-https://youtu.be/j78eKkp5IqI
Link of Lecture 18 :-https://youtu.be/4xQBVCejNRQ
Link of Lecture 19 :-https://youtu.be/qemVEllOYXs
Link of Lecture 20 :-https://youtu.be/cRHGAnPir04
Link of Lecture 21 :-https://youtu.be/MUAw5sUKYpE
Link of Lecture 22 :-https://youtu.be/7i6U4ESKdtY
Link of Lecture 23 :-https://youtu.be/SYa6XHc-2ig
Link of Lecture 24 :-https://youtu.be/4MckyKLP14s
Link of Lecture 25 :-https://youtu.be/yR0fQNUY8_c
Link of Lecture 26 :-https://youtu.be/SPBB122ssdU
Link of Lecture 27 :-https://youtu.be/lLFNDms0P5U
Link of Lecture 28 :-https://youtu.be/ovZnpjBKSBI
Link of Lecture 29 :-https://youtu.be/3c8WMU5_JPU
Link of Lecture 30 :-https://youtu.be/TVZMM3wq_kg
Link of Lecture 31 :-https://youtu.be/ZRIwzpg-VRw
Link of Lecture 32 :-https://youtu.be/LeKJmiYu6PI
Link of Lecture 33 :-https://youtu.be/28vu-NB9nPA
Link of Lecture 34 :-https://youtu.be/9ddtltUn-lQ
Link of Lecture 35 :-https://youtu.be/RR2ypAqGv2M
Link of Lecture 36 :-https://youtu.be/6t4Wf4fgS1I
Link of Lecture 37 :-https://youtu.be/TXroae8Ql0Y
Link of Lecture 38 :-https://youtu.be/2KbscnqquoA
Link of Lecture 39 :-https://youtu.be/UVwXR6MgPZ4
Link of Lecture 40 :-https://youtu.be/5WikJWYHPpY
Link of Lecture 41 :-https://youtu.be/x6gDluMo69Y
Link of Lecture 42 :-https://youtu.be/Is-vic8uJm0
Link of Lecture 43 :-https://youtu.be/jCYIBO31LlQ
Link of Lecture 44 :-https://youtu.be/53YomTYgGB4
Link of Lecture 45 :-https://youtu.be/dWyT6Q2SeAU
Link of Lecture 46 :-https://youtu.be/Brf7D5fosWo
Link of Lecture 47 :-https://youtu.be/EuUes9iT94E
Link of Lecture 48 :-https://youtu.be/FXbRkMZJIzg
Link of Lecture 49 :-https://youtu.be/UQL0YaBXyp0
Link of Lecture 50 :-https://youtu.be/PrnvOnat8_4
Link of Lecture 51 :-https://youtu.be/D04PyG4m27o
Link of Lecture 52 :-https://youtu.be/7iPO3kYTv3U
Link of Lecture 53 :-https://youtu.be/-EQP7NWHFXQ
Link of Lecture 54 :-https://youtu.be/TPgi5FgjC_Y
Link of Lecture 55 :-https://youtu.be/zvoYQRIJgoM
Link of Lecture 56 :-https://youtu.be/aKOK9lOeJwM
Link of Lecture 57 :-https://youtu.be/kqJWwYbMGZ0
Link of Lecture 58 :-https://youtu.be/-hr6QgKGU_Y
Link of Lecture 59 :-https://youtu.be/JF9IhL12NFM
Link of Lecture 60 :-https://youtu.be/XafZjLC1tI8
Link of Lecture 61 :-https://youtu.be/wq7d7pFvVEw
Link of Lecture 62 :-https://youtu.be/y781iu2ed-Q
Link of Lecture 63 :-https://youtu.be/Xs8Je-JIhxg
Link of Lecture 64 :-https://youtu.be/OkIs_n7XL4E
Link of Lecture 65 :-https://youtu.be/KfFOtQaQdI4
Link of Lecture 66 :-https://youtu.be/Uk1NAL-kQCw
Link of Lecture 67 :-https://youtu.be/Ig-b5reG5Ew
Link of Lecture 68 :-https://youtu.be/fBqIc2bPjqY
Link of Lecture 69 :-https://youtu.be/hgp5oVocXvE
Link of Lecture 70 :-https://youtu.be/TlSxJsqgekQ
Link of Lecture 71 :-https://youtu.be/gOe4MaNTlZ0
Link of Playlist of Real Analysis : - https://www.youtube.com/playlist?list=PLayq03KnDhBHUNG3OST4yKH47rMW4_cqd
Видео Theorem 1: A monotone sequence of real numbers having a divergent subsequence is properly divergent. канала Epselon++
Theorem 1: A monotone sequence of real numbers having a divergent subsequence is properly divergent.
We provide a comprehensive explanation of this theorem, breaking it down step-by-step to ensure a clear understanding of its statement and implications. This theorem plays a crucial role in understanding the behavior of sequences in mathematical analysis, making it highly relevant for students and researchers.
This video will be especially useful for students pursuing BSc Mathematics or MSc Mathematics, as well as those preparing for competitive exams like CSIR NET, GATE, IIT JAM, TIFR, and other similar examinations. Mastering this theorem will enhance your conceptual clarity and problem-solving skills in sequence-related topics.
Timestamps:-
0:00 – Introduction to the theorem and its importance
1:10 – Definitions of monotone sequences and divergent subsequences
2:30 – Statement of the theorem
3:15 – Step-by-step explanation of the theorem’s proof
5:00 – Examples to illustrate the theorem
5:45 – Summary and key takeaways
#mscmaths
#bscmaths
#csirnetmaths
#iitjam
Chapter 5 Real Sequence
Link of Lecture 1 :- https://youtu.be/TaRTAVTvrMU
Link of Lecture 2 :- https://youtu.be/nq-Pa-lrWWM
Link of Lecture 3 :- https://youtu.be/8g0HX7W6eLo
Link of Lecture 4 :- https://youtu.be/B9phcAf3cgk
Link of Lecture 5 :- https://youtu.be/gcV7VFctaD8
Link of Lecture 6 :- https://youtu.be/vI7biPhry18
Link of Lecture 7 :- https://youtu.be/mFBYP7NjJOs
Link of Lecture 8 :- https://youtu.be/4RcxgM-WIVI
Link of Lecture 9 :- https://youtu.be/IaRr91cAp4g
Link of Lecture 10 :-https://youtu.be/INAgmY4phJg
Link of Lecture 11 :-https://youtu.be/m3eHHEM6nTw
Link of Lecture 12 :-https://youtu.be/AOx6OJKvTB0
Link of Lecture 13 :-https://youtu.be/oexcSOxxM9c
Link of Lecture 14 :-https://youtu.be/Oyi75_7BBZY
Link of Lecture 15 :-https://youtu.be/kzzEyNGqceE
Link of Lecture 16 :-https://youtu.be/Ly2rNBnd3aw
Link of Lecture 17 :-https://youtu.be/j78eKkp5IqI
Link of Lecture 18 :-https://youtu.be/4xQBVCejNRQ
Link of Lecture 19 :-https://youtu.be/qemVEllOYXs
Link of Lecture 20 :-https://youtu.be/cRHGAnPir04
Link of Lecture 21 :-https://youtu.be/MUAw5sUKYpE
Link of Lecture 22 :-https://youtu.be/7i6U4ESKdtY
Link of Lecture 23 :-https://youtu.be/SYa6XHc-2ig
Link of Lecture 24 :-https://youtu.be/4MckyKLP14s
Link of Lecture 25 :-https://youtu.be/yR0fQNUY8_c
Link of Lecture 26 :-https://youtu.be/SPBB122ssdU
Link of Lecture 27 :-https://youtu.be/lLFNDms0P5U
Link of Lecture 28 :-https://youtu.be/ovZnpjBKSBI
Link of Lecture 29 :-https://youtu.be/3c8WMU5_JPU
Link of Lecture 30 :-https://youtu.be/TVZMM3wq_kg
Link of Lecture 31 :-https://youtu.be/ZRIwzpg-VRw
Link of Lecture 32 :-https://youtu.be/LeKJmiYu6PI
Link of Lecture 33 :-https://youtu.be/28vu-NB9nPA
Link of Lecture 34 :-https://youtu.be/9ddtltUn-lQ
Link of Lecture 35 :-https://youtu.be/RR2ypAqGv2M
Link of Lecture 36 :-https://youtu.be/6t4Wf4fgS1I
Link of Lecture 37 :-https://youtu.be/TXroae8Ql0Y
Link of Lecture 38 :-https://youtu.be/2KbscnqquoA
Link of Lecture 39 :-https://youtu.be/UVwXR6MgPZ4
Link of Lecture 40 :-https://youtu.be/5WikJWYHPpY
Link of Lecture 41 :-https://youtu.be/x6gDluMo69Y
Link of Lecture 42 :-https://youtu.be/Is-vic8uJm0
Link of Lecture 43 :-https://youtu.be/jCYIBO31LlQ
Link of Lecture 44 :-https://youtu.be/53YomTYgGB4
Link of Lecture 45 :-https://youtu.be/dWyT6Q2SeAU
Link of Lecture 46 :-https://youtu.be/Brf7D5fosWo
Link of Lecture 47 :-https://youtu.be/EuUes9iT94E
Link of Lecture 48 :-https://youtu.be/FXbRkMZJIzg
Link of Lecture 49 :-https://youtu.be/UQL0YaBXyp0
Link of Lecture 50 :-https://youtu.be/PrnvOnat8_4
Link of Lecture 51 :-https://youtu.be/D04PyG4m27o
Link of Lecture 52 :-https://youtu.be/7iPO3kYTv3U
Link of Lecture 53 :-https://youtu.be/-EQP7NWHFXQ
Link of Lecture 54 :-https://youtu.be/TPgi5FgjC_Y
Link of Lecture 55 :-https://youtu.be/zvoYQRIJgoM
Link of Lecture 56 :-https://youtu.be/aKOK9lOeJwM
Link of Lecture 57 :-https://youtu.be/kqJWwYbMGZ0
Link of Lecture 58 :-https://youtu.be/-hr6QgKGU_Y
Link of Lecture 59 :-https://youtu.be/JF9IhL12NFM
Link of Lecture 60 :-https://youtu.be/XafZjLC1tI8
Link of Lecture 61 :-https://youtu.be/wq7d7pFvVEw
Link of Lecture 62 :-https://youtu.be/y781iu2ed-Q
Link of Lecture 63 :-https://youtu.be/Xs8Je-JIhxg
Link of Lecture 64 :-https://youtu.be/OkIs_n7XL4E
Link of Lecture 65 :-https://youtu.be/KfFOtQaQdI4
Link of Lecture 66 :-https://youtu.be/Uk1NAL-kQCw
Link of Lecture 67 :-https://youtu.be/Ig-b5reG5Ew
Link of Lecture 68 :-https://youtu.be/fBqIc2bPjqY
Link of Lecture 69 :-https://youtu.be/hgp5oVocXvE
Link of Lecture 70 :-https://youtu.be/TlSxJsqgekQ
Link of Lecture 71 :-https://youtu.be/gOe4MaNTlZ0
Link of Playlist of Real Analysis : - https://www.youtube.com/playlist?list=PLayq03KnDhBHUNG3OST4yKH47rMW4_cqd
Видео Theorem 1: A monotone sequence of real numbers having a divergent subsequence is properly divergent. канала Epselon++
monotone sequence divergent subsequence properly divergent sequence real numbers real analysis BSc mathematics MSc mathematics CSIR NET preparation GATE mathematics IIT JAM TIFR mathematical theorems proof of theorems monotone sequence theorem sequences in real analysis convergence divergence limit points sequence behavior exam preparation competitive mathematics exams Epselon++ channel monotonicity in sequences advanced mathematics
Комментарии отсутствуют
Информация о видео
18 января 2025 г. 19:39:46
00:06:44
Другие видео канала
Linear congruences | incongruent solution | congruence | number theory | lecture 28 | bsc | msc
cauchy first theorem on limits | cauchy second theorem on limits | cesaro theorem of sequence
Linear congruences | Linear congruence | congruence | number theory | lecture 26 | bsc | msc | maths
bounded sequence in real analysis | bounded sequence example |
gauss test for convergence | gauss test for convergence of series
if series is convergent then xn tends to zero
question on limit superior and limit inferior
Bolzano weierstrass theorem converse | converse of bolzano weierstrass theorem | examples
how to find limit point of a set | set 1 | lecture 40 | limit point |
monotonic sequence | monotonic sequence examples | monotonic sequence in real analysis
null sequence in real analysis | null sequence | null sequence examples |
lower and upper bounds | real analysis | lower and upper bound of a set | #shorts
examples of convergent sequence | question on convergence of sequence | bsc | msc |
bolzano weierstrass theorem | bolzano weierstrass property | proof | bsc | msc
If a set S is closed and bounded then Sup S and Inf S belongs to the set S | Proof |
convergence of geometric series | convergence of geometric series proof |
Introduction to Real Analysis | Chapter 1 Set Theory |Compliment of set- Universal Set & Ven Diagram
laplace transform Question 14 | find the laplace transform of ∫ (1 - e^-2x) dx from x=0 to x=t
sequence ratio test | ratio test for sequences | un+1/un |
congruence modulo n | if ma=mb mod n, (m,n)=d, d=dn' then a=b mod n' | theorem 10| congruence mod n
monotonic sequence | monotonic sequence examples | monotonic sequence in real analysis
