nonstandard analysis

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

不可算名詞

(mathematical analysis) Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials.

日本語の意味

非標準解析：ハイパー実数体系に基づく解析学の一分野で、無限小量（特に微分）を厳密に定義・利用する数学的解析。

英語の意味

(mathematical analysis) Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials.

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Her research in nonstandard analysis provided new insights into the rigorous use of infinitesimals in calculus.

彼女の非標準解析の研究は、微積分における無限小の厳密な利用に新たな洞察をもたらした。

詳細

意味（1）

(mathematical analysis) Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials.

To be sure, the epsilon-delta methods arose in part because mathematicians became unsure of the foundational validity of infinitesimals. But since nonstandard analysis exactly provides the missing legitimacy, the original motivation for adopting epsilon-delta arguments appears to fall away.

詳細