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数学概念和规律是解题、证题的依据,离开它们,解题、证题就成了空话。但是有些概念和规律,从纯数学的观点看,是正确的,用于解决具体问题,情况可能发生变化。如求有理整函数的定义域,其自变量取值范围是一切实数。但是当自变量代表某一具体的几何量或物理量时,其取值范围不可能是一切实数,由于具体量的条件限制,有时不等于零,有时不能为负数。又如列方程解应用题,所求的根不一定是原方程的解,其解必须符合实际情况。有些概念和规律,在引入或推导论证过程中,可能增加一些附加条件,有时是为了便于分析或简化推导论证过程,当附加条件取消或改变,
Mathematical concepts and laws are the basis for solving problems and testifying questions. Leaving them out and solving problems and testifying questions become empty words. However, some concepts and laws are correct from the point of view of pure mathematics and are used to solve specific problems. The situation may change. If you want to have a domain of the whole function, the range of the arguments is all real numbers. However, when an independent variable represents a specific geometric quantity or physical quantity, the range of values cannot be all real numbers. Due to the limitation of the specific quantity, sometimes it is not equal to zero, and sometimes it cannot be negative. Another example is the solution of a column equation to an application. The root sought is not necessarily the solution of the original equation, and its solution must conform to the actual situation. Some concepts and laws may add some additional conditions during the introduction or deduction of the argument, sometimes to facilitate the analysis or simplify the deduction process, when the conditions are cancelled or changed.