Supremum

• Prove That Every Nonnegative Real Number Has an nth Root
  Use completeness and continuity to prove that for every a ≥ 0 and positive integer n, some nonnegative b satisfies bⁿ = a.
• 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.
• How to Calculate the Supremum of a Set
  To calculate a supremum, find an upper bound and prove set elements come arbitrarily close to it; unlike a maximum, the supremum need not belong to the set.