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3. Associating One Item with Another: Functions

  • 2020
  • OriginalPaper
  • Chapter
Published in:
Author
David Makinson
Published in
Sets, Logic and Maths for Computing
Publisher
Springer International Publishing

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Abstract

In this chapter we introduce the basic concepts needed in order to work with functions. We begin with the intuitive idea of a function and its mathematical definition as a special kind of relation. We then see how general concepts for relations play out in this particular case (domain, range, restriction, image, closure, composition, inverse) and distinguish some important kinds of function (injective, surjective, bijective). These concepts permit us to link functions with counting, via the principles of equinumerosity, comparison and the surprisingly versatile pigeonhole rule. Finally, we identify some very simple kinds of function that appear over and again (identity, constant, projection, characteristic and choice functions), and explain the use of functions to represent sequences and families.

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previous chapter Comparing Things: Relations
next chapter Recycling Outputs as Inputs: Induction and Recursion
Title
Associating One Item with Another: Functions
Author
David Makinson
Copyright Year
2020
Book
Sets, Logic and Maths for Computing

Print ISBN: 978-3-030-42217-2

Electronic ISBN: 978-3-030-42218-9

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-42218-9_3

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