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Intro to Real Analysis - Video 11: Sequence limit laws, uniqueness, squeeze thm
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Intro to Real Analysis (aka 'Baby' Real Analysis). This video covers limit laws for sequences, uniqueness of a limit, squeeze theorem, and proofs of some of the limit laws.
Timestamps
0:00 Discussion of Limit Laws
2:00 Discussion of Squeeze Theorem for Sequences
6:08 Two Important Propositions
6:38 Proof of Limit Law 1 (Convergence of Constant Sequence)
8:27 Strategy for Proving Limit Law 2 (Constant Multiple Rule for Convergence)
11:45 Actual Proof of Limit Law 2
16:12 Strategy for Proving Limit Law 3 (Sum/Difference Law)
28:40 Actual Proof of Limit Law 3
Texts/references:
1) Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings
2) Introduction to Real Analysis 4th ed. by Bartle & Sherbert
3) Principles of Mathematical Analysis 3rd Ed. by Rudin (aka 'Baby Rudin')
Timestamps
0:00 Discussion of Limit Laws
2:00 Discussion of Squeeze Theorem for Sequences
6:08 Two Important Propositions
6:38 Proof of Limit Law 1 (Convergence of Constant Sequence)
8:27 Strategy for Proving Limit Law 2 (Constant Multiple Rule for Convergence)
11:45 Actual Proof of Limit Law 2
16:12 Strategy for Proving Limit Law 3 (Sum/Difference Law)
28:40 Actual Proof of Limit Law 3
Texts/references:
1) Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings
2) Introduction to Real Analysis 4th ed. by Bartle & Sherbert
3) Principles of Mathematical Analysis 3rd Ed. by Rudin (aka 'Baby Rudin')