Real Sequences Intro 2

This is second and the last lecture on the series of Introductory Lectures on Real Sequences. As remarked in the first one, I advise everybody to view these two lectures before starting on Real Sequences -- Lecture-N series. Sukumar D Jul 23, 2021, 5:50 PM (13 hours ago) to me Real Sequence Intro 1 https://youtu.be/RAdedpuPMJI 0:00 Intro 0:46 Inherent nature of Analysis 8:54 Approximation property of rationals in reals (Density of rationals) 13:30 Motivation for convergence of sequence 19:50 Definition of a sequence and notation 23:43 Examples of real sequence 32:44 Convergence of sequence, (Analytic, geometric and graphic) 41:50 How to go about proving the convergence? 44:50 First example convergent sequence and estimation 56:52 An example of non convergent sequence 1:04:30 Motivation for Cauchy sequence. _______________________________________ Real Sequence Intro 2 https://youtu.be/IuRxKSQq-9w 0:00 Intro 1:03 Picture proof of a theorem 12:16 Textbook proof of unique limit 17:32 Aliter 19:43 Curry leave trick and triangle inequality static vs dynamic version 26:20 Replacing first N elements of the sequence 32:10 Absolute values of a converging sequence 36:08 Sequence converging to 0 and its absolute values 45:05 Sequence converging to a negative/positive real number 1:00:42 When the terms of the sequence negative/positive 1:05:52 Converging sequences are bounded sequences 1:11:07 Summary