2. Introduction
The chapter focuses on advanced concepts in discrete mathematics, including properties of functions, equivalence relations, and combinatorial functions such as the Stirling function. It covers injective, surjective, and bijective functions in detail and provides various proof concepts relevant to these topics. Key exercises and activities enhance understanding through application of theories discussed.
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Sections
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What we have learnt
- Surjective functions need not be bijective unless the sets involved are finite.
- Equivalence relations can partition a set into subsets of equal size.
- The Stirling function type 2 counts the ways to partition a set into non-empty disjoint subsets.
Key Concepts
- -- Injective Function
- A function where each element of the domain maps to a unique element of the codomain.
- -- Surjective Function
- A function where every element of the codomain is mapped by at least one element from the domain.
- -- Bijective Function
- A function that is both injective and surjective, establishing a one-to-one correspondence between the domain and codomain.
- -- Stirling Function
- A function representing the number of ways to partition a set of r elements into s non-empty subsets.
- -- Equivalence Relation
- A relation that is reflexive, symmetric, and transitive, partitioning a set into equivalence classes.
Additional Learning Materials
Supplementary resources to enhance your learning experience.