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实数与数轴上的点是一一对应的.由此我想到了这样一个问题:实数与数轴上的点的个数是否可以比较?有同学认为这两个数量无限多,无法比较.而我认为它们的个数是一样多的.虽然实数有无限多个,数轴是一条直线,直线上的点同样有无限多个,但不论任何实数,都能在数轴上找到与之对应的点,所以说它们的个数一样多.因此,在无限范围内考虑问题,与在有限范围内得出的结论是全然不同的.
There is a one-to-one correspondence between real numbers and points on the number axis. So I thought of the question: Is the number of points on the real number and number axes comparable? Some students think that these two numbers are infinite and cannot be compared. And I think The number of them is the same. Although the real number has infinite number, the number axis is a straight line, and the point on the straight line is also infinitely many, but regardless of any real number, the corresponding point can be found on the number axis, so There are as many of them. Therefore, considering the problem in an infinite range is totally different from the conclusion drawn in a limited range.