一本数学书或讲义,首先应当是正确的,不含糊的。但我们从经验中知道,一个毫不含糊的正确的证明,即使提出的问题本身是有意义的,仍然可以远不能令人满意;它也可能显得呆板,令人厌倦或者失望。一个在各方面都可以接受的叙述,它最容易犯的毛病就是“凑巧”。在进一步讨论以前,我要给出一个具体的例子,我们看看下面一个并不十分初等的定理的证明。设叙列a_1,a_2,…,的项都是非负的,不全为零的实数,则证。用定义数c_1,c_2,…,然后用算术平均与几何平均之间的不等式,最后用定义数e的叙列的一般项[(k+1)/k]~k是增加的事实,我们就得到 A math book or handout should first be correct and unambiguous. However, we know from experience that an unambiguous and correct proof, even if it raises questions that are meaningful in itself, can still be far from satisfactory; it can also be dull, tiring, or disappointing. A narrative that can be accepted in all aspects is the most likely to make a mistake. Before further discussion, I would like to give a concrete example. Let’s take a look at the proof of the following theorem, which is not very elementary. Suppose that the items of the a_list, a_2, ..., are non-negative, and real numbers that are not all zero are proof. Using the defined number c_1, c_2,..., and then using the inequality between the arithmetic average and the geometric mean, the fact that the general term [(k+1)/k]~k of the descriptive number e is increased, we get