Shows what it means for a sequence to be monotone and also gives examples. Basically if a sequence is either increasing or decreasing for each consecutive term it is monotone. (cc)

Uses some other vocabulary including divergence and convergence, but the main information involved shows what it means to be a subsequence of a set, (cc)

Exercises

1. Describe all subsequences and monotonic subsequences of the sequence 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0…….

Thomson.Bruckner, Bruckner; Section 2.11, Problem 2.11.9

2.  Prove that every unbounded sequence has a strictly monotonic subsequence (increasing or decreasing)     Thomson, Bruckner, and Bruckner; Section 2.11, Problem 2.11.18

3. Show that every subsequence of a subsequence of a sequence {xn} is itself a subsequence of{xn}

Thomson, Bruckner, and Bruckner; Section 2.11, Problem 2.11.2

4. Describe all sequences that have only infinitely many different subsequences.

Thomson, Bruckner, and Bruckner; Section 2.11, Problem 2.11.5