Abstract
This chapter provides an introduction to the fundamental building blocks in mathematics such as sets, relations and functions. Sets are collections of well-defined objects, relations indicate relationships between members of two sets A and B and functions are a special type of relation where there is exactly or at most one relationship for each element a Î A with an element in B.
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Notes
- 1.
We distinguish between total and partial functions. A total function f:A ® B is defined for every element in A whereas a partial function may be undefined for one or more values in A.
- 2.
There are mathematical objects known as multi-sets or bags that allow duplication of elements. For example, a bag of marbles may contain three green marbles, two blue and one red marble.
- 3.
The British logician, John Venn, invented the Venn diagram. It provides a visual representation of a set and the various set theoretical operations. Their use is limited to the representation of two or three sets as they become cumbersome with a larger number of sets.
- 4.
The natural numbers, integers and rational numbers are countable sets whereas the real and complex numbers are uncountable sets.
- 5.
Cartesian product is named after René Descartes who was a famous 17th French mathematician and philosopher. He invented the Cartesian coordinates system that links geometry and algebra, and allows geometric shapes to be defined by algebraic equations.
- 6.
Parnas made important contributions to software engineering in the 1970s. He invented information hiding which is used in object-oriented design.
- 7.
We distinguish between total and partial functions. A total function f:A ® B is defined for all elements in A whereas a partial function may be undefined for one or more elements in A.
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© 2013 Springer-Verlag London
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O’Regan, G. (2013). Sets, Relations and Functions. In: Mathematics in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-4534-9_2
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DOI: https://doi.org/10.1007/978-1-4471-4534-9_2
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