Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Examples for the association of algebraic and rational numbers.

If this page is mystical to you return to the previous page for an explanation of the notation and issue.

Any rational number x=p/q is the solution of qx-p=0, where q is positive. Thus we have

.

For example,

.

The square root of two is the solution of

.

Clearly, for this equation,

.

However, this equation has two roots, the square root of two, and its negative (which we agreed to count first). Thus

.

Fine print, your comments, more links, Peter Alfeld, PA1UM

[16-Aug-1996]