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柳暗花明又一村:无穷小重返数学舞台 17世纪下半叶,牛顿、莱布尼兹创立的微积分学,用了无穷小量的概念,但因对其解释含糊不清,出现了贝克莱悖论,导致数学史上的“第二次数学危机”。19世纪,柯西、维尔斯特拉期等人引入极限论、实数论,使微积分理论严格化,从而避免了贝克莱悖论,圆满解决了第二次数学危机。然而与此同时,极限方法代替了无限小量方法。无穷小量作为“消失了量的幽魂”被排斥在数学殿堂之外了。
Wicked again another village: Infinitesimal return to the mathematical stage In the second half of the 17th century, Newton, Leibniz’s calculus, with an infinitesimal concept, but due to its ambiguous interpretation, appeared Berkeley paradox , Leading to the “second mathematical crisis” in the history of mathematics. In the 19th century, Cauchy and Wilstras introduced the limit theory and real number theory, which made the theory of calculus rigorous, thus avoiding Berkeley paradox and satisfactorily solving the second mathematical crisis. At the same time, however, the limit method replaces the infinitesimal method. Infinitesimals were excluded from the math hall as “ghosts that disappeared.”