bolzano weierstrass theorem | bolzano weierstrass property | proof | bsc | msc

bolzano weierstrass theorem | bolzano weierstrass property | proof | bsc | msc

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Links of the other videos

Chapter 3
Link of Lecture 1 :-    • neighbourhood of a point in real anal...  
Link of Lecture 2 :-    • Union of two neighbourhood of x is ne...  
Link of Lecture 3 :-    • Intersection of two neighbourhood of ...  
Link of Lecture 4 :-    • infinite intersection of (-1/n,1/n) |...  
Link of Lecture 5 :-    • Infinite Intersection of neighbourhoo...  
Link of Lecture 6 :-    • Interior of a set | real analysis | I...  
Link of Lecture 7 :-    • open sets in real analysis | bsc | ms...  
Link of Lecture 8 :-    • Theorem :- If S is subset of R then S...  
Link of Lecture 9 :-    • Theorem : union of open sets is open ...  
Link of Lecture 10 :-   • intersection of two open sets is open...  
Link of Lecture 11 :-   • interior set is an open set | proof |...  
Link of Lecture 12 :-   • interior set is largest open subset o...  
Link of Lecture 13 :-   • prove that every open interval is ope...  
Link of Lecture 14 :-   • limit point of a set | deleted neighb...  
Link of Lecture 15 :-   • Examples of limit point of set | limi...  
Link of Lecture 16 :-   • Theorem 1 on limit point of set | use...  
Link of Lecture 17 :-   • limit point | a finite set has no lim...  
Link of Lecture 18 :-   • every interior point of a set is limi...  
Link of Lecture 19 :-   • Derived set | real analysis | derived...  
Link of Lecture 20 :-   • Derived set | Properties | Theorem  |...  
Link of Lecture 21 :-   • Theorem 1 on limit point of set | use...  
Link of Lecture 22 :-   • Theorem 2 on limit point of set | use...  
Link of Lecture 23 :-   • closed set real analysis | closed set...  
Link of Lecture 24 :-   • Union of two closed set is closed | p...  
Link of Lecture 25 :-   • Intersection of two closed set is clo...  
Link of Lecture 26 :-   • a set is closed iff its complement is...  
Link of Lecture 27 :-   • If a set S is closed and bounded then...  
Link of Lecture 28 :-   • adherent point | adherent point in re...  
Link of Lecture 29 :-   • A Set is Closed iff it is equal to it...  
Link of Lecture 30 :-   • Theorem : Closure of A is the smalles...  
Link of Lecture 31 :-   • properties of closure of a set | theo...  
Link of Lecture 32 :-   • intersection and union of interior of...  
Link of Lecture 33 :-   • Relation between closure of set and i...  
Link of Lecture 34 :-   • Dense sets | perfect set | examples o...  
Link of Lecture 35 :-   • A set is dense iff it intersect every...  
Link of Lecture 36 :-   • bolzano weierstrass theorem | bolzano...  
Link of Lecture 37 :-   • how to find limit point of a set | se...  
Link of Lecture 38 :-   • how to find limit point of a set | se...  
Link of Lecture 39 :-   • how to find limit point of a set | se...  
Link of Lecture 40 :-   • how to find limit point of a set | se...  

Link of Playlist of Real Analysis : -    • Real Analysis by Mr Akash Singh | SK ...  

Timestamps:-
00:00 - Introduction to Bolzano-Weierstrass property
00:45 - Statement of the Bolzano-Weierstrass theorem
01:30 - Discussion on bounded sequences
02:15 - Definition of limit points
03:00 - Importance of accumulation points in the theorem
03:45 - Step 1: Constructing a bounded sequence example
04:30 - Step 2: Defining subsequences and their role
05:15 - Explanation of convergent subsequences
06:00 - Visualizing the proof with diagrams
06:45 - Step 3: Applying the Bolzano-Weierstrass property
07:30 - Detailed breakdown of the proof structure
08:15 - Handling different cases in the proof
09:00 - Step 4: Proving the existence of a limit point
09:45 - Subsequence convergence proof
10:30 - Understanding bounded intervals
11:15 - Applying the property to real-world problems
12:00 - Common misconceptions about the theorem
12:45 - Step 5: Conclusion of the proof
13:30 - Examples illustrating the theorem
14:15 - Summary and key takeaways

This will guide your viewers through the video efficiently.

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