Surreal Numbers – An Introduction

by Claus Tøndering

Surreal numbers are fascinating for several reasons. They are built on an extremely simple and small foundation, and yet they provide virtually all of the capabilities of ordinary real numbers. With surreal numbers we are able to (or rather, required to) actually prove things we normally take for granted, such as “x = x” or “x = y ⇒ x + z = y + z”. Furthermore, surreal numbers extend the real numbers with a tangible concept of infinity and infinitesimals (numbers that are smaller than any positive real number, and yet are greater than zero). With surreal numbers it makes sense to talk about “infinity minus 3”,“infinity to the third power”, or “the square root of infinity”.

49 pages, ebook

First published January 25, 2005