有时,判断处理一个问题的方法对不对,不一定是很容易的。如证明0.9=1,用下面的证法对吗? 0.9×10=9.999……① -)0.9×1=0.999……②①-②得0.(?)×9=9,所以0.(?)=9/9=1。在这里,0.(?)实质上表示无限个小数的和。由②得出①,必须对这里的无限个数的和运用乘法分配律。这样做是不是允许呢?是不是对任何“无限个数的和”都能运用我们熟悉的运算定律? 下面的例子似乎提示我们:可以作出肯定的回 Sometimes it is not always easy to judge how to deal with a problem. If the proof 0.9 = 1, with the following proof of right? 0.9 × 10 = 9.999 ...... ① -) 0.9 × 1 = 0.999 ...... ② ①-② have 0. (?) × 9 = 9, so 0. (? ) = 9/9 = 1. Here, 0 (?) Essentially means the sum of an infinite number of decimals. From ②, we must apply the law of multiplication to the infinite number here. Is this allowed? Is it possible to apply our familiar law of operations to any “infinite number of sums”? The following example seems to suggest that we can make a positive return