1951 AMC 12 第 14 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
14.
关于几何证明，请指出下列哪一项说法不正确：
In connection with proof in geometry, indicate which one of the following statements is incorrect:
有些陈述无需证明即可接受。
Some statements are accepted without being proved.
在某些情况下，证明某些命题时存在不止一种正确的步骤顺序。
In some instances there is more than one correct order in proving certain propositions.
证明中使用的每一个术语都必须事先定义。
Every term used in a proof must have been defined previously.
如果已知条件中含有一个不真实的命题，就不可能通过正确推理得出真实的结论。
It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposition.
只要存在两个或更多互相矛盾的命题，就可以使用间接证明。
Indirect proof can be used whenever there are two or more contrary propositions.
答案：C
小提示：
区分未经定义的原始术语与未经证明的公理
Distinguish undefined primitive terms from unproved axioms
大提示：
公理系统若要定义每一个术语，就会陷入无限倒推
An axiomatic system cannot define every term without an infinite regress
解答：
公理化体系以有意不加定义的原始术语以及无需证明即可接受的陈述为起点。因此，“证明中的每一个术语都必须事先定义”这一说法不正确。
因此，题目预期的正确答案是 C。
An axiomatic development begins with primitive terms that are deliberately left undefined, as well as statements accepted without proof. Therefore it is not true that every term in a proof must previously have been defined.
Thus, the intended correct answer is C.
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