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College Math Resources - Topics in Precalculus

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The Real Number System

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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.