English Dictionary

completeness axiom

名詞

(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).

日本語の意味

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

The completeness axiom guarantees that every nonempty set of real numbers that is bounded above has a least upper bound in the real numbers.

完備性公理は、有界上側を持つ任意の非空の実数集合に対して、その最小上界（上限）が実数の中に存在することを保証する。

意味（1）

(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).

completeness axioms （ plural ）