Proof: Monotone Sequence has Monotone Subsequences | Real Analysis

We prove if a sequence is monotone then all of its subsequences are monotone. In particular, we prove that all subsequences of an increasing sequence are increasing and all subsequences of a decreasing sequence are decreasing. We prove this using the definition of a monotone sequence. #RealAnalysis

Intro to Subsequences:    • Intro to Subsequences | Real Analysis  
What are Monotone Sequences?    • What are Monotone Sequences? | Real A...  
Monotone Subsequence Theorem:    • Monotone Subsequence Theorem (Every S...  
Monotone Sequence Converges if it has Convergent Subsequence:    • Monotone Sequence with Convergent Sub...  
Monotone Convergence Theorem:    • Detailed Proof of the Monotone Conver...  

Real Analysis Playlist:    • Real Analysis  

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