魯賓遜與萊布尼茲

    上世紀60年代，魯賓遜深入研讀萊布尼茲數學手稿，有許多發現。

    魯賓遜高度讚美萊布尼茲關於實無窮小的創新思想，推崇他為現代非標準分析的先行者。

    本文附件，記錄了魯賓遜的原話，請讀者一閱。

袁萌  陳啟清 元月10日

附件：

Abraham Robinson. He wrote:

[...] the idea of infinitely small or infinitesimal quantities seems to appeal naturally to our intuition. At any rate, the use of infinitesimals was widespread during the formative stages of the Differential and Integral Calculus. As for the objection [...] that the distance between two distinct real numbers cannot be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or infinitely large compared with the real numbers but which were to possess the same properties as the latter

Robinson argued that this law of continuity of Leibniz's is a precursor of the transfer principle. Robinson continued:（以下省略）