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《反证法三则》一文的有些内容似有待商榷。(该文刊载于《数学教学通讯》1981年第1期)现对该文提出两点看法,共同探讨,并请指正。一、三个例题是否不能用直接证法证明? 该文说:“在几何与代数中,都有一些不能用直接证法证明而只能用反证法才能证明的题目,除前面所举的例题(笔者注:即下面例1)外,下面再举二例(笔者注:即下面例2、例3)。”现试用直接证法证明
Some of the contents of the “Three Anti-Certification Law” article seem to be debatable. (The article is published in “Mathematics Teaching Newsletter” No. 1 in 1981.) Now I put forward two points of view on the article, discuss together, and correct me. Whether one or three example questions cannot be proved by direct proofs? The article states: “In geometry and algebra, there are some problems that cannot be proved by direct proof but only by means of counterevidence, except for the examples cited above ( The author’s Note: In the following example 1), two examples are given below (author’s note: the following example 2 and 3).”