Produced by Charles Wells Revised 2017-03-04 Introduction to this website website TOC website index blog

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.

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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