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一.引言 連續函數不一定可微分,而且有的連續函數處處不可微分,最早舉出這種例子的是Weier-strass,他的例子是: F(x)=sum from n=0 to +∞(b~n cos(a~nπx)), (a是奇数,01+3π/2) (1)比較新的一個例子是van der Waerden所舉出的,那就是 f(x)=sum from n=I to +∞(fn(x)), (2)其中f_n(x)表示從x到離x最近的分數m/10~n(m是任意整數)的距離,有了這兩個例子,製造處處不可微分的連續两數的問題便已經是圓滿地解决了。
I. INTRODUCTION Continuous functions are not necessarily differentiable, and some continuous functions are not irreducible everywhere. The earliest example of this is Weier-strass. His example is: F(x)=sum from n=0 to +∞( b~n cos(a~nπx)), (a is an odd number, 01+3π/2) (1) A newer example is given by van der Waerden, that is f (x)=sum from n=I to +∞(fn(x)), (2) where f_n(x) represents the distance from x to the nearest score m/10~n (m is any integer) from x, With these two examples, the problem of irreducible consecutive numbers in the manufacturing sector has been successfully resolved.