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- W1040691816 abstract "Very many counting problems can be formulated in terms of counting the number of functions between two sets (possibly satisfying certain properties) or counting the number of subsets of a given set (possibly satisfying certain properties). In this chapter we give a brief introduction to these ideas. They naturally lead to the binomial coefficients , one of the most important families of numbers in all mathematics. Counting sets of functions Suppose that X and Y are finite sets. It is natural to ask how many different functions there are with domain X and codomain Y . For example, if X is a set of people and Y is a set of dishes on a menu, then each function X → Y represents a choice of (one) dish for each person, so that the number of functions represents the number of possible orders by the set of people. If S is a set of students and T is a set of tutors then a function S → T is an assignment of a tutor for each student. There is another increased level of abstraction here. The idea of treating a set, for example the set of integers, as a single mathematical object is one stage of abstraction. A further stage is viewing a function from one set to another as a single mathematical object. But now we are forming a new set whose elements are the functions from one set to another and asking questions about this set." @default.
- W1040691816 created "2016-06-24" @default.
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- W1040691816 date "1997-12-11" @default.
- W1040691816 modified "2023-09-27" @default.
- W1040691816 title "Counting functions and subsets" @default.
- W1040691816 doi "https://doi.org/10.1017/cbo9780511801136.015" @default.
- W1040691816 hasPublicationYear "1997" @default.
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