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Mathematics-Online course: Basic Mathematics - Real Numbers

# Supremum and Infimum

A subset of is bounded above if there is exists a bound such that

The completeness axiom in guarantees the existence of a least upper bound, denoted by

Note that the supremum does not necessarily have to belong to . Thus, sets that are bounded above are not required to contain a maximal element .

Analogously lower bounds are defined; the greatest lower bound is denoted by , and a minimal element is denoted by .

(Authors: Höllig/Kopf/Abele)