唐好色
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加入时间: 2006/03/20
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作者：唐好色 在 驴鸣镇 发贴, 来自 http://www.hjclub.org
You first rigorously define limit which is a real number. Notice the definition of limit involves only real numbers. There are NO infinitesimals,
http://en.wikipedia.org/wiki/%28%CE%B5,_%CE%B4%29-definition_of_limit
Then use that definition of limit to define dy/dx. dy/dx is one entity, not a quotient of two numbers. It is useful to write it as a quotient for computational reasons, but it is NOT a quotient.
In fact, Newton used the notation of y'.
Here is the irony. dy/dx is a far superior notation for computational purpose, but it is also conceptually misleading because it looks like a quotient.
Newton's y' notation is conceptually better, but it is bad for computation.
This is the reason freshman calculus sticks mostly with dy/dx.
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Another distraction: After calculus was invented, there was a big fight over credits between Newton and Leibniz. For nationalistic pride, the British mathematicians closed ranks with Newton while the continental mathematicians supported Leibniz. British mathematics suffered a great deal simply because they insisted on using Newton's y' while the continental mathematicians went with the misleading but computationally superior dy/dx notation.
作者：唐好色 在 驴鸣镇 发贴, 来自 http://www.hjclub.org |
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