Last Updated：2025/11/28

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

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nonstandard analysis

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Source Word

nonstandard analysis

Noun

uncountable

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

Japanese Meaning

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。

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

Google Translation / DeepL Translation

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。

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(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.

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nonstandard analysis

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nonstandard analysis

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