数学家自古以来就无法解释无限小的问题

来源: fourwaves 于 2016-06-05 14:38:08 [档案] [旧帖] [给我悄悄话] 本文已被阅读：次 (5078 bytes)

回答: 牛顿不发表自己的发现，从后来的结果看，是因为还不完善由 bridge008 于 2016-06-05 10:08:35

是牛顿启发了数学家要解释自然界必须用无限小。莱才努力从数学的角度发展出他的微积分。

In early calculus the use of infinitesimal quantities was thought unrigorous, and was fiercely criticized by a number of authors, most notably Michel Rolle and Bishop Berkeley. Berkeley famously described infinitesimals as the ghosts of departed quantities in his book The Analyst in 1734. Working out a rigorous foundation for calculus occupied mathematicians for much of the century following Newton and Leibniz, and is still to some extent an active area of research today.

For centuries, mathematicians and philosophers wrestled with paradoxes involving division by zero or sums of infinitely many numbers. These questions arise in the study of motion and area. The ancient Greek philosopher Zeno of Elea gave several famous examples of such paradoxes. Calculus provides tools, especially the limit and the infinite series, which resolve the paradoxes.