What are suprema and infima of a set? This is an important concept in real analysis, we'll be defining both terms today with supremum examples and infimum examples to help make it clear! In short, a supremum of a set is a least upper bound. An infimum is a greatest lower bound. It is easily proven that we can refer to "the supremum" and "the infimum" of a set because if they exist they are unique.

Epsilon Definition of Supremum and Infimum:    • Epsilon Definition of Supremum and In...  
Proof that suprema and infima are unique:    • Proof: Supremum and Infimum are Uniqu...  
Proof the maximum of a set is the supremum:    • Proof: Maximum of a Set is the Suprem...  
Absolute value inequality result we mention near the end of the lesson:    • Proof: A Useful Absolute Value Inequa...  

Supremum and Infimum Example Exercises:
   • Proof: Supremum of {1/n} = 1 | Real A...  
   • Supremum of the Union of Sets | Real ...  
   • Proof: Supremum of {1/n} = 1 | Real A...  
   • Proof: Minimum of a Set is the Infimu...  
   • Proof: Infimum of {1/n} = 0 | Real An...  
   • Prove Infimums Exist with the Complet...  

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