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	主题: 關於“否定之否定”的笑話

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關於“否定之否定”的笑話

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Infinitesimals weren't rigorously defined until 1960's. -- 唐好色 - (527 Byte) 2010-5-05 周三, 下午3:15 (181 reads)

唐好色
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标题: On mathematical standards (128 reads) 时间: 2010-5-06 周四, 上午12:04

作者：唐好色 在驴鸣镇发贴, 来自 http://www.hjclub.org

It took about 100 years for mathematicians to lay a rigorous definition for limit upon which calculus rests. It was a very hard problem. This problem in the early 19th century was as hard as the problem of rigorously defining Feynman path integral is today. By the time of Cauchy/Weierstrass, the problem was pretty much cleaned up by banishing infinitesimals. However this was only for mathematicians. Even today, the epsilon-delta definition of limit is one of the hardest concepts for an undergraduate to grasp.

The problem with liberal arts people is that they are not trained to think carefully and rigorously. Minor logic holes are acceptable to them. It is a matter of weighing the evidence. However mathematics does not work this way.

The standard of rigor in mathematics is orders of magnitude higher. Liberal arts people and "social scientists" like Marx did not understand that then and they do not understand that now.

作者：唐好色 在驴鸣镇发贴, 来自 http://www.hjclub.org

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