Last Updated
：2025/11/26
completeness axiom
Noun
Japanese Meaning
順序体において、任意の部分集合が上界を持つ場合、その部分集合の最小の上界（すなわち上限）が必ず存在し、さらにその上限が順序体の要素であることを定めた公理
Sense（1）
（ plural ）
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(mathematics) The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).
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completeness axiom
The completeness axiom guarantees that every nonempty set of real numbers that is bounded above has a least upper bound in the real numbers.
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The completeness axiom guarantees that every nonempty set of real numbers that is bounded above has a least upper bound in the real numbers.
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