In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian products in terms of ordered pairs. In this section we introduced relations as subsets of Cartesian products. Thus we can now define functions in a way that depends only on the concept of set. Although this definition is not obviously related to the way we usually work with functions in mathematics, it is satisfying from a theoretical point of view, and computer scientists like it because it is particularly well suited for operating with functions on a computer. Definition A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties: 1. For every element x in A, there is an element y in B such that (x, y) E F. 2. For all elements x in A and y and z in B, if (x, y) EFand (x, z) E F, then y z.

In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian products in terms of ordered pairs. In this section we introduced relations as subsets of Cartesian products. Thus we can now define functions in a way that depends only on the concept of set. Although this definition is not obviously related to the way we usually work with functions in mathematics, it is satisfying from a theoretical point of view, and computer scientists like it because it is particularly well suited for operating with functions on a computer. Definition A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties: 1. For every element x in A, there is an element y in B such that (x, y) E F. 2. For all elements x in A and y and z in B, if (x, y) EFand (x, z) E F, then y z.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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