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据说有个外国人发表了一项声明,宣布他证明了一个非常有趣的定理:“在所有正整数中,1是最大的正整数。”下面就是他的证明。证明假设1不是最大的正整数,则必存在一个正整数k满足k>1,上式两端同时乘上正整数k,可得k~2>k。因为k是正整数.故k~2也是正整数,即说明还存在一个正整数k~2大于k,故k不可能是最大的正整数。由此即得任何比1大的正整数都不可能是最大的正整数,因此,只剩下1是最大的正整数了。 1是最大的正整数,岂不荒谬?
A foreigner is said to have issued a statement announcing that he proved a very interesting theorem: “In all positive integers, 1 is the largest positive integer.” Here is his proof. To prove that hypothesis 1 is not the largest positive integer, there must be a positive integer k satisfying k>1, and both ends of the equation are multiplied by a positive integer k at the same time, and k~2>k can be obtained. Since k is a positive integer, k~2 is also a positive integer, which means there is still a positive integer k~2 greater than k, so k cannot be the largest positive integer. Thus, any positive integer larger than 1 is unlikely to be the largest positive integer, so only 1 is the largest positive integer. 1 is the largest positive integer, isn’t it ridiculous?