Here we dissect a theorem statement about convergent sequences from Rudin's Principles of Mathematical Analysis (a.k.a. Baby Rudin). There is a lot to unpack here, including some allusions to Topology.
//Books
A great companion text to Rudin is Maxwell Rosenlicht's Introduction to Analysis. The explanations are a lot clearer and the book is under $20.
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Walter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUis
Gerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6Np
R. Shankar - Principles of Quantum Mechanics - amzn.to/40825xj
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//Reference for Cantor’s Work
www.ias.ac.in/article/fulltex...
//Exercises
- Show that the elements of the Cantor set can be written in base-3 as 0.a_1 a_2 a_3 … where each a_i is either 0 or 2.
//Watch Next
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0:00 Introduction
0:40 Anticipating Topology
1:48 Proof of Part A
3:53 Can a sequence converge to more than one point?
5:17 Proof of Part B
8:21 Using a Theorem Backwards
8:47 Functional Analysis Example
10:28 What about a PROOF?
Негізгі бет An Introduction to Sequences in Real Analysis
Пікірлер: 10