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In calculus, the (ε, δ)-definition of limit ("epsilon-delta definition of limit") is a formalization of the notion of limit. It was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy never gave an () definition of limit in his Cours d'Analyse, but occasionally used arguments in proofs. The definitive modern statement was ultimately provided by Karl Weierstrass.〔 〕〔. Accessed 2009-05-01.〕 ==History== Isaac Newton was aware, in the context of the derivative concept, that the limit of the ratio of evanescent quantities was ''not'' itself a ratio, as when he wrote: :Those ultimate ratios ... are not actually ratios of ultimate quantities, but limits ... which they can approach so closely that their difference is less than any given quantity... Occasionally Newton explained limits in terms similar to the epsilon-delta definition. Augustin-Louis Cauchy gave a definition of limit in terms of a more primitive notion he called a ''variable quantity''. He never gave an epsilon-delta definition of limit (Grabiner 1981). Some of Cauchy's proofs contain indications of the epsilon-delta method. Whether or not his foundational approach can be considered a harbinger of Weierstrass's is a subject of scholarly dispute. Grabiner feels that it is, while Schubring (2005) disagrees.〔 Nakane concludes that Cauchy and Weierstrass gave the same name to different notions of limit.〔Nakane, Michiyo. Did Weierstrass's differential calculus have a limit-avoiding character? His definition of a limit in ε−δ style. BSHM Bull. 29 (2014), no. 1, 51–59.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「(ε, δ)-definition of limit」の詳細全文を読む スポンサード リンク
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