O'Reilly logo

The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

III.41 Irrational and Transcendental Numbers

Ben Green

An irrational number is one that cannot be written as a / b with both a and b integers. A great many naturally occurring numbers, such as Image, e, and π, are irrational. The following proof that Image is irrational is one of the best-known arguments in all of mathematics. Suppose that Image = a / b; since common factors can be canceled, we may assume that a and b have no common factor; we have a2 = 2b2, which ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required