The Exponent Zero

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. The Exponent Zero

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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The Exponent Zero

What should $a^0$ be? Multiplying it by $a$ gives

\

by property (1) of exponents. Solving $a^0 \ for $a^0$ then gives
\

Again, we must have $a>0$ for this to make sense.

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