College Math Resources - Topics in Precalculus

The Real Number System

What are the 'Transcendental' Numbers?

            Transcendental numbers are real numbers that do not satisfy any polynomial equation with rational coefficients.

            Examples include pi and the number  e  that is used as the base for natural logartihms.
But irrational surds such as root two are not transcendental since any root is defined as the solution of a polynomial equation. (eg root two is the positive solution of x-squared=2)

            You might find  proofs that pi and e are transcendental in an introductory Analysis text, or by exploring the links to various web-based analysis course materials.

 If you have come across any good web-based illustrations of these and related concepts,
     please do let us know and we will add them here.