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看这些方程时，你可能会问零的0次幂是多少。这是一个很好的问题，答案实际上正在被讨论。组合学(Combinatorics)需要0^0 = 1或者空函数(empty function)不存在。有些人认为0^0应该是一种不定形式。这是许多人在微积分(calculus入门课上学到的，通常是在学生开始学习洛必达法则(L'Hopital rule)时学到的。然而，0^0 = 1的一个很大的论据来自《具体数学》(Concrete Mathematics),一些教科书没有定义0^0这个量，因为当x减少到0时，函数0^x和x^0有不同的极限值。但这是一个错误。如果二项式定理在x=0，y=0，和x/y或x=-y时有效，我们必须为所有x定义x^0=1。这个定理太重要了，不能任意限制！相比之下，0^x函数就不那么重要了。(《具体数学(第二版)》第162页)。我们相信0^0 = 1，但是，如果你在微积分课上，从左边和右边看x^0的极限，看看会发生什么。
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When looking at these equations you may ask what zero to the power of zero is. This is a great question and the answer is actually being debated. Combinatorics needs 0^0 = 1 or the empty function can not exist. Some people believe that 0^0 should be an indeterminate form. This is what many people are taught in beginning calculus classes and is generally taught when students begin to learn about L'Hopital's rule. However, a great argument for 0^0 = 1 comes from Concrete Mathematics (Graham, Knuth, Patashnik) Some textbooks leave the quantity 0^0 undefined, because the functions 0^x and x^0 have different limiting values when x decreases to 0. But this is a mistake. We must define x^0=1 for all x , if the binomial theorem is to be valid when x=0 , y=0 , and/or x=-y . The theorem is too important to be arbitrarily restricted! By contrast, the function 0^x is quite unimportant. (p.162) We believe that 0^0 = 1, however, if you are in a calculus class look at the limits of x^0 from both the left and the right and see what happens.
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当知识之圆不断扩大，未知的边界亦会同样增加。
As our circle of knowledge expands,so does the circumference of darkness surrounding it.
标签不是科普是科学性
当知识之圆不断扩大，未知的边界亦会同样增加。
As our circle of knowledge expands,so does the circumference of darkness surrounding it.
矮油，梗了梗了
无事勿争，安然度日
Pay tribute to life ! Live for the future.
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