of Math

Fall 2007

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

last modified Saturday September 8 2007 12:02 pm EDT