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有理数有了合理的代数意义后,大家自然就会问:它是否有几何意义呢?答案是肯定的.在一条水平直线上,取一截线段作为单位长度,若令它的左端点和右端点分别表示0和1,则整数就可以用这条直线上的间隔为单位长度的点的集合来表示,正整数在0的右侧,负整数在0的左侧.以q为分母的分数,可以用单位长度分为q等份的点来表示.于是,每一个有理数都与直线上的一个点相对应.人们曾经误以为,直线上的所有的点都
Rational numbers have a reasonable algebraic meaning, we naturally ask: Is it geometric? The answer is yes, in a horizontal line, take a line segment as a unit length, if it is the left and right ends Respectively, 0 and 1, then the integer can be expressed in terms of the set of points on the line whose unit length is an integer, the positive integer is to the right of 0 and the negative integer is to the left of 0. The fraction with q as the denominator, Can be expressed in terms of the unit length divided by q, so that every rational number corresponds to a point on a straight line.People mistakenly assume that all the points on the line