The important thing is that these numbers can be represented as points on a number line (the real number line) with zero at the centre, positive numbers to the right of zero and negative numbers to the left.
To understand why this is the case, consider the number +1 on the real number line. If +1 is multiplied by -1 the result is -1 or a 'counter clockwise rotation' about the origin of 180[degrees].
For numbers on the real number line
, there is a definite sense of order.
Schenk begins with an explanation of the real number line
and guides readers through instructions on multiplication division and trigonometric functions where he unveils the mysteries of triangles.
Recall that the real number line consists of all rational and irrational numbers, each representing a point on the line, the distance from the origin to the point.
A single point p in the real number line. Clearly p can be contained in a closed interval of arbitrarily small length.
After all, the real number line
is an infinitely long, continuous expanse, while the counting numbers are just isolated milestones along this line.
Call this the real number line. No matter how close two numbers be, others are always between them.
IN A WORLD WHERE ESTABLISHED religion and political theories have taken a beating and come out sullied by compromises, failures and hypocrisies, the realness of the real number line and the immutability of prime numbers have a strong appeal.
* Analysis studies functions, the real number line
, and the ideas of continuity and limit.