Supremum and infimum

• Find the Supremum, Infimum, lim sup, and lim inf of 2 − 1/n
  For n ≥ 1, the sequence 2 − 1/n has infimum and minimum 1, supremum 2, and both lim sup and lim inf equal to 2.
• Does Every Nonempty Bounded-Above Set of Real Numbers Have a Supremum?
  Every nonempty subset of the real numbers that is bounded above has a supremum, by the completeness property of the real numbers.