一般人都会认为0.999……这个无限循环小数不等于1,它比1小,虽然它越来越接近1,但永远都到不了1。有人说,0.999……就是1,很多人都知道如何证明:0.333……=1/3,两边都乘以3,结果就是0.999……等于1。还有一个更诡异的例子:1-1+1-1+1-1+……是多少?如果这样变换:(1-1)+(1-1)+(1-1)+……-0+0+0+……它就等于0。如果这样变换:1-(1-1)-(1-1)-(1-1)-……-1-0-0-0……它就等于1。出现这种情况,肯定要从无限上找原 Most people will think 0.999 ...... This infinite loop fraction is not equal to 1, it is smaller than 1, although it is closer to 1, but never can not 1. Some people say that 0.999 ... is 1, and many people know how to prove that: 0.333 ... = 1/3, multiplied by 3 on both sides, the result is 0.999 ... equal to 1. There is a more strange example: 1-1 + 1-1 + 1-1 + ... is how much? If so transformed: (1-1) + (1-1) + (1-1) + ... - 0 + 0 + 0 + ... it is equal to 0. If you change this way: 1- (1-1) - (1-1) - (1-1) - ... -1-0-0-0 ... it is equal to one. This happens, we must find the original infinite