What are Monotone Sequences? | Real Analysis

We introduce monotone sequences, monotone increasing, and monotone decreasing sequences, with plenty of examples and non-examples. We'll see how a sequence can be both increasing and decreasing, and we'll see some equivalent characterizations of increasing and decreasing sequences. #RealAnalysis

We'll also discuss what it means for a sequence to be strictly increasing and strictly decreasing, and what it means to be eventually increasing and eventually decreasing.

Proof of Monotone Convergence Theorem:    • Detailed Proof of the Monotone Conver...  
Fun Example of Monotone Convergence Theorem:    • Using the Monotone Convergence Theore...  
Monotone Sequence Converges if it has Convergent Subsequence:    • Monotone Sequence with Convergent Sub...  

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