I. Remarks on the Single Independent Variable x

Abstract

I am beginning systematically in such a way that I will not speak of functions at all, but instead introduce the independent variable x and represent it in the usual manner as a point on the x-axis whose distance fromthe origin is |x| units of measurement and which lies to the right of the origin for positive values of x and to the left of the origin for negative ones. I wish to direct your attention to the precision of the construction of such a point. I note in this respect: If I use an empirical procedure such as drawing, measuring, evaluating by eye, or mental reproduction by spatial perception, the result of the construction only has limited accuracy; I will prove this for measuring, by showing some numerical values.

Abstract

I am beginning systematically in such a way that I will not speak of functions at all, but instead introduce the independent variable x and represent it in the usual manner as a point on the x-axis whose distance fromthe origin is |x| units of measurement and which lies to the right of the origin for positive values of x and to the left of the origin for negative ones. I wish to direct your attention to the precision of the construction of such a point. I note in this respect: If I use an empirical procedure such as drawing, measuring, evaluating by eye, or mental reproduction by spatial perception, the result of the construction only has limited accuracy; I will prove this for measuring, by showing some numerical values.