Abstract
The concept of function is introduced along with the related nomenclature: domain, independent variable, image, range and synonyms. Surjective, injective, invertible or one-to-one functions are considered and illustrated by examples. The study of the abstract functions provides the opportunity to define equipotent sets and, as a consequence, infinite sets and finite sets. Some examples are examined. First properties of composite functions are considered. Restriction and extension of a function are defined.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Chinn, W.G., Steenrod, N.E.: First Concepts of Topology. Random House, New Mathematical Library, New York (1966)
Gowers, T.: Mathematics: A Very Short Introduction. Oxford University Press (2002)
Singh, S.: Fermat’s Last Theorem. Simon Singh (1997)
Ventre, A.: Matematica. Fondamenti e Calcolo. Wolters Kluwer, Milano (2021)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ventre, A.G.S. (2023). Functions. In: Calculus and Linear Algebra. Springer, Cham. https://doi.org/10.1007/978-3-031-20549-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-20549-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-20548-4
Online ISBN: 978-3-031-20549-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)