Whirlwind Tour
of Math

Fall 2007

Irrational Numbers

Can every number be written as a ratio of two whole numbers? (That is, as a fraction.) The answer is no. Many numbers---in fact most numbers, in a sense we'll discuss when we consider the infinite---cannot be expressed as fractions. Such numbers are "irrational." In this topic we'll develop tools for deciding whether a given number is irrational and see how irrational numbers fit into the number system.
This is the first topic for which we'll use Stillwell's Yearning for the Impossible. Imaginary Numbers, The Infinitesimal and The Infinite are others. The common thread through these topics is that of mathematics struggling to incorporate new ideas.
http://cs.marlboro.edu/ courses/ fall2007/math_tour/ irrational
last modified Saturday September 8 2007 12:02 pm EDT