Infimum and supremum

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In mathematics, the infimum or greatest lower bound of a set A, written as , is the greatest element among all lower bounds of A. Similarly, the supremum or least upper bound of A, written as , is the smallest element among all upper bounds of A.[1]

For example, if A is the set , then and . Infimum and supremum are unique, if they exist.[2][3] Infimum and supremum are key concepts in the field of mathematical analysis.

Related pages[change | change source]

References[change | change source]

  1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-10-14.
  2. Weisstein, Eric W. "Supremum". mathworld.wolfram.com. Retrieved 2020-10-14.
  3. Weisstein, Eric W. "Infimum". mathworld.wolfram.com. Retrieved 2020-10-14.