What is 0^0? - Introduction

Editor's note: This article was published in March 2008.

When calculus books state that 0⁰ is an indeterminate form, they mean that there are functions f(x) and g(x) such that f(x) approaches 0 and g(x) approaches 0 as x approaches 0, and that one must evaluate the limit of [f(x)]^g(x) as x approaches 0. But what if 0 is just a number? Then, we argue, the value is perfectly well-defined, contrary to what many texts say. In fact, 0⁰ = 1!