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Limit-free derivatives

Published online by Cambridge University Press:  23 January 2015

Christopher J. Sangwin
Christopher J. Sangwin*
Affiliation:
MSOR Network, School of Mathematics, University of Birmingham, Birmingham B15 2TT e-mail:, [email protected]
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Extract

Algebraic double roots are used by [1] to motivate the following limit-free definition of derivative:

‘A function f(x) has a derivative m at x = a if

for some value c.’

As we shall see later, ‘function’ in this definition will actually be restricted to real polynomials and [1] concludes

‘We have shown how an elementary algebraic principle — double roots — can lead to a complete calculus of polynomials and related functions, without the need for a limit concept.

Type
Articles
Information
The Mathematical Gazette , Volume 95 , Issue 534 , November 2011 , pp. 469 - 482
Copyright
Copyright © The Mathematical Association 2011

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