Functions 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.
Functions 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.
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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Question
Please help me answer how is number 1 (For every element x in A, there is an element y in B such that (x,y) is in F )
differ from a relation? Please explain this!
Transcribed Image Text:am looking for you to think about
the implications of the first one.
How does this differ from a relation? Do
Transcribed Image Text:Functions
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.
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