Abstract
Combinatorics is the study of finite sets. To define finite sets, we need the notion of bijective function. Given two sets X and Y, a function f : X → Y is injective or one-to-one if f(a) ≠ f(b) for any a, b ∈ X with a ≠ b. A function f : X → Y is surjective or onto if for any y ∈ Y, there exist x ∈ X such that f(x) = y. A function is bijective if it is injective and surjective. A function f : X → Y is invertible if there exists a function g : Y → X such that f(x) = y if and only if g(y) = x. If g exists, it is called the inverse of f and it is usually denoted by f−1. We leave as an exercise the fact that a function is bijective if and only if it is invertible.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2009 Hindustan Book Agency
About this chapter
Cite this chapter
Cioabă, S.M., Murty, M.R. (2009). Recurrence Relations. In: A First Course in Graph Theory and Combinatorics. Texts and Readings in Mathematics, vol 55. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-39-2_2
Download citation
DOI: https://doi.org/10.1007/978-93-86279-39-2_2
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-98-2
Online ISBN: 978-93-86279-39-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)