Sets

• What Are the Minimum, Maximum, Infimum, and Supremum?
  Learn how minimum, maximum, infimum, and supremum differ, with definitions, examples, and a test for whether a bound is attained.
• Difference Between Supremum and Upper Bounds
  An upper bound is any number above a set, while its supremum is the least such number; infimum is the greatest lower bound.
• What Is an Example of an Unbounded Set?
  The natural numbers are an example of an unbounded set: no finite real number is an upper bound for all of their elements.
• Can 7 Drinks with 7 Flavors Make Infinite Varieties?
  With continuously variable proportions, seven flavors produce uncountably many mathematical mixtures; counting only flavor subsets gives 127 nonempty choices.
• What Is the Difference Between Bounded, Unbounded, Open, and Closed Sets?
  Open, closed, bounded, and unbounded describe different properties. Learn their definitions, classify common subsets of the real line, and avoid common mix-ups.