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Produced by Charles Wells     Revised 2017-03-04
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FUNCTIONS

Overview

The concept of function in mathe­matics is as important as any mathe­matical idea. The mathe­matician's concept of function includes the kinds of functions you studied in calculus but is much more abstract and general.

Like every part of abstract­math, the chapter on functions is designed to get you started thinking about functions. It is no way complete. Wikipedia has much more complete coverage of mathe­matical functions, scattered over many articles.

Contents

This chapter has seven sections:

• Examples of functions. Intended to raise your consciousness about the wide variety of things mathe­maticians call "functions''.
• Specification and definition of function. It is necessary to know the precise definition of function in order to prove theorems about functions.
• Notation and terminology for functions. The terminology used to define functions and the basic concepts connected with functions.
• Properties of functions. Some of the properties functions can have.
• Images and metaphors for functions. The many ways mathe­maticians understand functions.
• Representations of continuous functions
• Representations of discrete functions
• Derivatives

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