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大家都知道,极限理論是数学分析的重要基础。可是目前普通中学高中二年級代数課里讲授关于极限的知識却不是系统地讲授极限的理論,而主要地是为了中学数学教材中某些知識(例如,代数中的无穷递縮等比数列所有項的和、循环小数化分数、无理指数等;几何中的圓周长、圓面积以及其他图形的面积或体积等)的需要。自然,这些教材也会給进一步学习数学分析作准备的。这一部分教材包括有:数列的极限、变量(不連續的)的极限、有关极限的几个定理以及无穷递缩等比数列所有項的和与循环小数化分数等。由于在中学数学里,不是系統地介紹有关极限的知識,是在处理某些問題的时候,需要一些极限知識,而这些問题又只涉及不連续的变量的极限,因之教材
As we all know, limit theory is an important foundation for mathematical analysis. However, the current knowledge about the limit in the second-grade algebra class of ordinary high school senior middle school is not the theory of systematically teaching the limit, but mainly for some knowledge in the middle school mathematics textbook (for example, the infinite number of analogy in algebra is equal to all the items in the series. The sum of the sum, the fractionalization fraction, the irrational index, etc.; the length of the circle in the geometry, the area of the circle, and the area or volume of other figures, etc.). Naturally, these textbooks will also prepare for further study of mathematical analysis. This part of the textbook includes: the limits of the series, the limits of the variables (discontinuous), several theorems about the limit, and the sum of all the items of the infinitely-reduced geometric series and the fractionalization of the loop. Since in middle school mathematics, the knowledge about limits is not systematically introduced, some limit knowledge is needed when dealing with certain problems, and these problems only involve the limits of discontinuous variables.