Proof: Infimum of {1/n} = 0 | Real Analysis

The infimum of the set containing all reciprocals of natural numbers has an infimum of 0. That is, 0 is the greatest lower bound of {1/n | n is natural}. We prove this infimum in today's real analysis lesson using the Archimedean Principle, which tells us that given any real number x, we can find a greater natural number.

Proof of Archimedean Principle:    • Proof: Archimedean Principle of Real Numbe...  
Definition of Supremum and Infimum of a Set:    • Definition of Supremum and Infimum of a Se...  
Epsilon Definition of Supremum and Infimum:    • Epsilon Definition of Supremum and Infimum...  

Real Analysis Playlist:    • Real Analysis  

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