基于数轴的实数知识重构
Reconstruction of Real Number Knowledge Based on the Number Line

本文主要谈论了“实数单位”是什么的问题。通过单位线段OA在OA延长线上的运动，从几何直观得到“1”是自然数的单位。在对自然数单位“1”的组合与拆分的过程中，进一步加深了对进位制的理解，并且通过对“1”的等分得到了分数单位。将整数和分数形式统一，得到了有理数的概念。使单位线段做反向运动得到表示负有理数的点。通过对小数数位的分析得到，在OA线段所在的直线上，每一个无限不循环小数总能找到一条线段与之对应。因此，无理数的单位也是“1”。最终，得到实数的单位为“1”。研究实数单位对理解数的概念的一致性和数与式运算的一致性都有着深刻的意义。
This article mainly talks about the question of what a “real unit” is. Through the movement of OA on the extension line of the unit line segment, it is intuitively obtained from the geometry that “1” is the unit of natural numbers. In the process of combining and splitting the natural number unit “1”, the understanding of the carry system is further deepened, and the fractional unit is obtained by dividing the “1”. The whole number and fraction form are unified, and the concept of rational numbers is obtained. Make the unit line segment move in the opposite direction to get a point representing a negative rational number. Through the analysis of decimal places, it is obtained that on the straight line where the OA line segment is located, each infinite non-cyclic decimal can always find a line segment corresponding to it. Therefore, the unit of an irrational number is also “1”. Eventually, the unit of the real number obtained is “1”. The study of real units is of profound significance for understanding the consistency of the concept of number and the consistency of number and formula operations.