SlideShare a Scribd company logo
Given the indexed collection of denumerable sets A_i with i N, prove that their union U_i N
A_i is also denumerable.
Solution
Given Ai is the denumerable sets
Union represents combination of all elements in all the sets
Hence U Ai has infinite many sets as Ai alone has infinite many sets
Hence U Ai is also denumerable

More Related Content

More from infomalad

How innovative offerings gain acceptance within market segmentsH.pdf
How innovative offerings gain acceptance within market segmentsH.pdfHow innovative offerings gain acceptance within market segmentsH.pdf
How innovative offerings gain acceptance within market segmentsH.pdf
infomalad
 
How does an organization socialize an individualHow ATM(automated.pdf
How does an organization socialize an individualHow ATM(automated.pdfHow does an organization socialize an individualHow ATM(automated.pdf
How does an organization socialize an individualHow ATM(automated.pdf
infomalad
 
Homework Develop a strategylies) to get a house. Consider possible h.pdf
Homework Develop a strategylies) to get a house. Consider possible h.pdfHomework Develop a strategylies) to get a house. Consider possible h.pdf
Homework Develop a strategylies) to get a house. Consider possible h.pdf
infomalad
 
Given a definition of a group Given a definition of a group.pdf
Given a definition of a group Given a definition of a group.pdfGiven a definition of a group Given a definition of a group.pdf
Given a definition of a group Given a definition of a group.pdf
infomalad
 
give an example of a successful progect thats ben done by a virtual .pdf
give an example of a successful progect thats ben done by a virtual .pdfgive an example of a successful progect thats ben done by a virtual .pdf
give an example of a successful progect thats ben done by a virtual .pdf
infomalad
 
File name a2.cppTaskFor this assignment, you are required to ei.pdf
File name a2.cppTaskFor this assignment, you are required to ei.pdfFile name a2.cppTaskFor this assignment, you are required to ei.pdf
File name a2.cppTaskFor this assignment, you are required to ei.pdf
infomalad
 
Explain in detail the DTE-DCE TransmissionSolutionData commun.pdf
Explain in detail the DTE-DCE TransmissionSolutionData commun.pdfExplain in detail the DTE-DCE TransmissionSolutionData commun.pdf
Explain in detail the DTE-DCE TransmissionSolutionData commun.pdf
infomalad
 
Find an example of a real project with a real project manager. The pr.pdf
Find an example of a real project with a real project manager. The pr.pdfFind an example of a real project with a real project manager. The pr.pdf
Find an example of a real project with a real project manager. The pr.pdf
infomalad
 
Discuss the importance of security and what elements need to be addr.pdf
Discuss the importance of security and what elements need to be addr.pdfDiscuss the importance of security and what elements need to be addr.pdf
Discuss the importance of security and what elements need to be addr.pdf
infomalad
 
Define financial engineering in terms of how to change the risk-retu.pdf
Define financial engineering in terms of how to change the risk-retu.pdfDefine financial engineering in terms of how to change the risk-retu.pdf
Define financial engineering in terms of how to change the risk-retu.pdf
infomalad
 
As a result of total quality management, organizational changes in t.pdf
As a result of total quality management, organizational changes in t.pdfAs a result of total quality management, organizational changes in t.pdf
As a result of total quality management, organizational changes in t.pdf
infomalad
 
Complete and balance the following redox equation. Show all work and.pdf
Complete and balance the following redox equation. Show all work and.pdfComplete and balance the following redox equation. Show all work and.pdf
Complete and balance the following redox equation. Show all work and.pdf
infomalad
 
Candidates for PPN include patients who ______. are also candidates .pdf
Candidates for PPN include patients who ______.  are also candidates .pdfCandidates for PPN include patients who ______.  are also candidates .pdf
Candidates for PPN include patients who ______. are also candidates .pdf
infomalad
 
Bulk movement of water across plasma membranes and the exchange of o.pdf
Bulk movement of water across plasma membranes and the exchange of o.pdfBulk movement of water across plasma membranes and the exchange of o.pdf
Bulk movement of water across plasma membranes and the exchange of o.pdf
infomalad
 
ANSWER ALL A positively charged ion with an equilibrium potential of.pdf
ANSWER ALL A positively charged ion with an equilibrium potential of.pdfANSWER ALL A positively charged ion with an equilibrium potential of.pdf
ANSWER ALL A positively charged ion with an equilibrium potential of.pdf
infomalad
 
A student can choose a computer project from one of three lists. The.pdf
A student can choose a computer project from one of three lists. The.pdfA student can choose a computer project from one of three lists. The.pdf
A student can choose a computer project from one of three lists. The.pdf
infomalad
 
7) Which reagent set could not be used to accomplish the transformati.pdf
7) Which reagent set could not be used to accomplish the transformati.pdf7) Which reagent set could not be used to accomplish the transformati.pdf
7) Which reagent set could not be used to accomplish the transformati.pdf
infomalad
 
12) The functional distribution of income measures which of the foll.pdf
12) The functional distribution of income measures which of the foll.pdf12) The functional distribution of income measures which of the foll.pdf
12) The functional distribution of income measures which of the foll.pdf
infomalad
 
Why is it important for financial managers to understand the valua.pdf
Why is it important for financial managers to understand the valua.pdfWhy is it important for financial managers to understand the valua.pdf
Why is it important for financial managers to understand the valua.pdf
infomalad
 
Why would a bulk forming process be chosen over a casting process to.pdf
Why would a bulk forming process be chosen over a casting process to.pdfWhy would a bulk forming process be chosen over a casting process to.pdf
Why would a bulk forming process be chosen over a casting process to.pdf
infomalad
 

More from infomalad (20)

How innovative offerings gain acceptance within market segmentsH.pdf
How innovative offerings gain acceptance within market segmentsH.pdfHow innovative offerings gain acceptance within market segmentsH.pdf
How innovative offerings gain acceptance within market segmentsH.pdf
 
How does an organization socialize an individualHow ATM(automated.pdf
How does an organization socialize an individualHow ATM(automated.pdfHow does an organization socialize an individualHow ATM(automated.pdf
How does an organization socialize an individualHow ATM(automated.pdf
 
Homework Develop a strategylies) to get a house. Consider possible h.pdf
Homework Develop a strategylies) to get a house. Consider possible h.pdfHomework Develop a strategylies) to get a house. Consider possible h.pdf
Homework Develop a strategylies) to get a house. Consider possible h.pdf
 
Given a definition of a group Given a definition of a group.pdf
Given a definition of a group Given a definition of a group.pdfGiven a definition of a group Given a definition of a group.pdf
Given a definition of a group Given a definition of a group.pdf
 
give an example of a successful progect thats ben done by a virtual .pdf
give an example of a successful progect thats ben done by a virtual .pdfgive an example of a successful progect thats ben done by a virtual .pdf
give an example of a successful progect thats ben done by a virtual .pdf
 
File name a2.cppTaskFor this assignment, you are required to ei.pdf
File name a2.cppTaskFor this assignment, you are required to ei.pdfFile name a2.cppTaskFor this assignment, you are required to ei.pdf
File name a2.cppTaskFor this assignment, you are required to ei.pdf
 
Explain in detail the DTE-DCE TransmissionSolutionData commun.pdf
Explain in detail the DTE-DCE TransmissionSolutionData commun.pdfExplain in detail the DTE-DCE TransmissionSolutionData commun.pdf
Explain in detail the DTE-DCE TransmissionSolutionData commun.pdf
 
Find an example of a real project with a real project manager. The pr.pdf
Find an example of a real project with a real project manager. The pr.pdfFind an example of a real project with a real project manager. The pr.pdf
Find an example of a real project with a real project manager. The pr.pdf
 
Discuss the importance of security and what elements need to be addr.pdf
Discuss the importance of security and what elements need to be addr.pdfDiscuss the importance of security and what elements need to be addr.pdf
Discuss the importance of security and what elements need to be addr.pdf
 
Define financial engineering in terms of how to change the risk-retu.pdf
Define financial engineering in terms of how to change the risk-retu.pdfDefine financial engineering in terms of how to change the risk-retu.pdf
Define financial engineering in terms of how to change the risk-retu.pdf
 
As a result of total quality management, organizational changes in t.pdf
As a result of total quality management, organizational changes in t.pdfAs a result of total quality management, organizational changes in t.pdf
As a result of total quality management, organizational changes in t.pdf
 
Complete and balance the following redox equation. Show all work and.pdf
Complete and balance the following redox equation. Show all work and.pdfComplete and balance the following redox equation. Show all work and.pdf
Complete and balance the following redox equation. Show all work and.pdf
 
Candidates for PPN include patients who ______. are also candidates .pdf
Candidates for PPN include patients who ______.  are also candidates .pdfCandidates for PPN include patients who ______.  are also candidates .pdf
Candidates for PPN include patients who ______. are also candidates .pdf
 
Bulk movement of water across plasma membranes and the exchange of o.pdf
Bulk movement of water across plasma membranes and the exchange of o.pdfBulk movement of water across plasma membranes and the exchange of o.pdf
Bulk movement of water across plasma membranes and the exchange of o.pdf
 
ANSWER ALL A positively charged ion with an equilibrium potential of.pdf
ANSWER ALL A positively charged ion with an equilibrium potential of.pdfANSWER ALL A positively charged ion with an equilibrium potential of.pdf
ANSWER ALL A positively charged ion with an equilibrium potential of.pdf
 
A student can choose a computer project from one of three lists. The.pdf
A student can choose a computer project from one of three lists. The.pdfA student can choose a computer project from one of three lists. The.pdf
A student can choose a computer project from one of three lists. The.pdf
 
7) Which reagent set could not be used to accomplish the transformati.pdf
7) Which reagent set could not be used to accomplish the transformati.pdf7) Which reagent set could not be used to accomplish the transformati.pdf
7) Which reagent set could not be used to accomplish the transformati.pdf
 
12) The functional distribution of income measures which of the foll.pdf
12) The functional distribution of income measures which of the foll.pdf12) The functional distribution of income measures which of the foll.pdf
12) The functional distribution of income measures which of the foll.pdf
 
Why is it important for financial managers to understand the valua.pdf
Why is it important for financial managers to understand the valua.pdfWhy is it important for financial managers to understand the valua.pdf
Why is it important for financial managers to understand the valua.pdf
 
Why would a bulk forming process be chosen over a casting process to.pdf
Why would a bulk forming process be chosen over a casting process to.pdfWhy would a bulk forming process be chosen over a casting process to.pdf
Why would a bulk forming process be chosen over a casting process to.pdf
 

Recently uploaded

Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
Thiyagu K
 
Additional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdfAdditional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdf
joachimlavalley1
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
Anna Sz.
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
Special education needs
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
Delapenabediema
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
MysoreMuleSoftMeetup
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
Celine George
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
Pavel ( NSTU)
 
Honest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptxHonest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptx
timhan337
 
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp NetworkIntroduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
TechSoup
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
Balvir Singh
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
Celine George
 
The approach at University of Liverpool.pptx
The approach at University of Liverpool.pptxThe approach at University of Liverpool.pptx
The approach at University of Liverpool.pptx
Jisc
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
Ashokrao Mane college of Pharmacy Peth-Vadgaon
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
JosvitaDsouza2
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
Jean Carlos Nunes Paixão
 
The French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free downloadThe French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free download
Vivekanand Anglo Vedic Academy
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
beazzy04
 
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
EugeneSaldivar
 

Recently uploaded (20)

Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
 
Additional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdfAdditional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdf
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
 
Honest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptxHonest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptx
 
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp NetworkIntroduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
 
The approach at University of Liverpool.pptx
The approach at University of Liverpool.pptxThe approach at University of Liverpool.pptx
The approach at University of Liverpool.pptx
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
 
The French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free downloadThe French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free download
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
 
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
 

Given the indexed collection of denumerable sets A_i with i N, prov.pdf

  • 1. Given the indexed collection of denumerable sets A_i with i N, prove that their union U_i N A_i is also denumerable. Solution Given Ai is the denumerable sets Union represents combination of all elements in all the sets Hence U Ai has infinite many sets as Ai alone has infinite many sets Hence U Ai is also denumerable