我們知道關於指數函數及對数函數的理論,古典的辦法,是以極限(?)為基礎的,這個辦法,正如Hardy所指出,有許多不方便處,因之,好些數學家(Hurwitz似乎是第一個)採取了別種辦法:他們將指数函數定義為對數函數的反函數,而將後者本身定義為一個積分 log x=integral from n=1 to x((1/t)dt)這個辦法,無疑是美麗的,這裏我們不擬細說它,我們只來提出另一個新辦法,即 We know the theory about the exponential function and the logarithmic function. The classical approach is based on the limit (?). This approach, as Hardy pointed out, has many inconveniences. Therefore, many mathematicians (Hurwitz seems to be The first one takes a different approach: they define the exponential function as an inverse function of the logarithmic function, and define the latter as an integral log x = integral from n = 1 to x ((1/t)dt). Undoubtedly beautiful, we don’t want to elaborate on it here, we only come up with another new method, namely