English Dictionary

Archimedean ordered field

名詞

(mathematics) An ordered field which satisfies the axiom of Archimedes.

日本語の意味

アルキメデスの公理を満たす順序体。すなわち、すべての正の元aに対して、ある自然数nが存在し、n倍したときに特定の基準を超えることが保証される体。

To develop a rigorous theory of limits, one often assumes the underlying number system is an Archimedean ordered field.

厳密な極限論を展開するために、基礎となる数体系がアルキメデスの公理を満たす順序体であると仮定することが多い。

意味（1）

(mathematics) An ordered field which satisfies the axiom of Archimedes.

The next axiom concerns [ x ], the integer part function. We have seen that this function plays a useful role in our theory, but it turns out that not all ordered fields have it defined. A field for which integer part is defined is called an Archimedean Ordered Field.

Archimedean ordered fields （ plural ）