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Russell, Bertrand (1872-1970)

Although this may seem a paradox, all exact science is dominated by the idea of approximation.

W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.

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Loci: Convergence

What is 0^0?

by Michael Huber and V. Frederick Rickey

Introduction

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!


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