If Sequence Diverges to Infinity then so do Subsequences | Real Analysis

A sequence diverges to infinity if and only if all of its subequences diverge to infinity. We prove this nice result about divergent sequences and divergent subsequences in today's real analysis video lesson by the river! #RealAnalysis #MathOutside

The proof proceeds simply with the definition of a sequence diverging to infinity. We only address positive infinity, the negative infinity proof is nearly identical and left as an exercise for the viewer.

Definition of Sequence Diverging to Infinity:    • Sequences that Diverge to Infinity (D...  
Intro to Subsequences:    • Intro to Subsequences | Real Analysis  
Sequence Converges if and only if all its Subsequences Do:    • Sequence Converges iff Every Subseque...  
Proof (-1)^n Diverges Using Subsequences:    • Sequence (1^n) Diverges using Subsequ...  
Important Fact about Subsequences (n_k \geq k):    • An Important Fact about Subsequences ...  

Real Analysis Playlist:    • Proof: Product of Absolute Values is ...  

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