／var／logmarcus chiu

Supremum (Least Upper Bound) - Infimum (Greatest Lower Bound)

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Supremum
(Least Upper Bound)
  • let 𝐹 be an ordered field and 𝑆⊆𝐹 be non-empty
  • the supremum of 𝑆, if it exists, is some 𝑏0∊𝐹 such that:
    • 𝑏0 is an upper bound of 𝑆
    • 𝑏0≤𝑏 for any other upper bound 𝑏 of 𝑆

Infimum
(Greatest Lower Bound)
  • let 𝐹 be an ordered field and 𝑆⊆𝐹 be non-empty
  • the infimum of 𝑆, if it exists, is some 𝑏0∊𝐹 such that:
    • 𝑏0 is a lower bound of 𝑆
    • 𝑏0≥𝑏 for any other lower bound 𝑏 of 𝑆