Can u please explain to me how is number 1 differ from a relation? Please don’t do the prove because I don’t need it, just explain how is it differ from a relation! Thank you my teacher wants me to think about the implications of number 1 so please help. Again NO PROOF NEEDED, I just want an explanation of how does number 1 differ from a relation?
Can u please explain to me how is number 1 differ from a relation? Please don’t do the prove because I don’t need it, just explain how is it differ from a relation! Thank you my teacher wants me to think about the implications of number 1 so please help. Again NO PROOF NEEDED, I just want an explanation of how does number 1 differ from a relation?
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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Can u please explain to me how is number 1 differ from a relation? Please don’t do the prove because I don’t need it, just explain how is it differ from a relation! Thank you my teacher wants me to think about the implications of number 1 so please help. Again NO PROOF NEEDED, I just want an explanation of how does number 1 differ from a relation?
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 \( (x, y) \in F \).
2. For all elements \( x \) in \( A \) and \( y \) and \( z \) in \( B \), if \( (x, y) \in F \) and \( (x, z) \in F \), then \( y = z \).
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