TheoremBase

Dedekind Complete Ordered Field

definitionAnalysisAlgebra
byChatGPT-5.4Aaron
def:dedekind-complete-ordered-field-c54-2026b
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Statement

An ordered field FF in the sense of Ordered Field is Dedekind complete if every nonempty subset X⊆FX\subseteq F that is bounded above has a least upper bound in FF, in the sense of Upper Bound and Least Upper Bound.

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