Set Theory By Naylor and Sell Homework Problems

In summary, the conversation is about understanding the approach to problems in a specific textbook on linear operator theory. The speaker is seeking help and advice from others who may have a good understanding of the textbook. They also discuss a question about the cardinality of sets and provide examples to support their answer. Ultimately, they conclude that the cardinality of the two sets is equal.
  • #1
fabbi007
20
0

Homework Statement



I am trying understand the approach to the problems given in the following textbook. Linear Operator Theory in Engineering and Science (Applied Mathematical Sciences) (Volume 0) [Paperback]
Arch W. Naylor (Author), George R. Sell (Author). Pages 12-29. There are excercise problems for which I need approach. Please let me know if anyone has a good understanding of them. Appreciate your response.

Homework Equations





The Attempt at a Solution

 
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  • #2
Speaking for myself, I don't have this book. If you have questions about one of the problems, post it here, along with your attempt at a solution.
 
  • #3
Is Card (N even)< Card (N)? Where N even is set of all even Natural numbers, N is set of all Natural numbers.

Hint: use the mapping from
N even to N is given by n-->n
a. Show examples of this mapping from
N even to N.

b. Is the mapping above onto? One-to-one?

My try at this question:

Since the mapping is n-->n it is the range of this mapping function is a proper subset of N hence the card (N even) <card (N) because there is one to one mapping and the N even maps into N.

Examples above mapping. 2->2, 4->4, 8->8, 268->268... Hence card(N even)< Card
 
  • #4
How about this mapping:
2 --> 1
4 --> 2
6 --> 3
8 --> 4
.
.
.
2k --> k
This mapping is 1-to-1 and onto. What does that say about the cardinality of the two sets?
 
  • #5
Mark44 said:
How about this mapping:
2 --> 1
4 --> 2
6 --> 3
8 --> 4
.
.
.
2k --> k
This mapping is 1-to-1 and onto. What does that say about the cardinality of the two sets?

They are equal!
 
  • #6
Yes.
 

Related to Set Theory By Naylor and Sell Homework Problems

1. What is set theory?

Set theory is a branch of mathematics that deals with the study of collections of objects, known as sets. It provides a foundation for other branches of mathematics and is used to define concepts such as functions, relations, and numbers.

2. Who are Naylor and Sell?

Naylor and Sell are the authors of the textbook "Set Theory By Naylor and Sell", which is commonly used as a reference for introductory courses in set theory. They are both mathematicians and educators, with extensive experience in teaching and research in the field of set theory.

3. What is the purpose of "Set Theory By Naylor and Sell Homework Problems"?

The purpose of "Set Theory By Naylor and Sell Homework Problems" is to provide additional practice and exercises for students studying set theory. It covers a range of topics and includes challenging problems to help students deepen their understanding and mastery of the subject.

4. How can I use "Set Theory By Naylor and Sell Homework Problems" effectively?

To use "Set Theory By Naylor and Sell Homework Problems" effectively, it is recommended to first read and understand the corresponding chapters in the textbook. Then, work through the problems in a systematic manner, using the solutions and explanations provided in the book to check your understanding and identify areas for improvement.

5. Is "Set Theory By Naylor and Sell Homework Problems" suitable for self-study?

While it is designed for use in a classroom setting, "Set Theory By Naylor and Sell Homework Problems" can also be used for self-study. However, it is recommended to have a basic understanding of set theory before attempting the problems, and it may be helpful to seek guidance from a teacher or tutor if needed.

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