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Positive Integer Exponents

The ``original'' definition of exponents which ``actually makes sense'' applies only to positive integer exponents:

$\displaystyle \zbox {a^n \isdef \underbrace{a\, a \, a \,\cdots \,a \, a}_{\mbox{$n$\ times}}}
$

where $ a>0$ is real.

Generalizing this definition involves first noting its abstract mathematical properties, and then making sure these properties are preserved in the generalization.


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``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 © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA