Subsequences and Bounded Sequences - 12
In this lecture, we’ll dive deeper into our study of sequences. First we’ll study the properties of subsequences (that is, infinite subsets of sequences) to learn when and how they might converge. We’ll see what additional conditions are necessary to guarantee that a bounded sequence converges.
Reading: Rudin Ch. 3: Subsequences (pg. 51-52), Cauchy sequences (pg. 52 and 55), Upper and Lower Limits (pg. 55-58)
Pre-Lecture Materials
- Subsequences and Bounded Sequences: Pre-lecture reading
- Subsequences and Bounded Sequences: Full Lecture Notes
Subsequences: Lecture video A
Bounded sequences and Cauchy sequences: Lecture video B
In-Class Activities
Open the following Overleaf link and make a copy for yourself. Remember to include the names of everyone who worked together in the document.
Lecture 12 In-Class Activity: Subsequences and Bounded Sequences
Assignments
- Submit Overleaf Proof 12: Convergence Properties of Sequences
- Homework 6