Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 1) a) prove that the union of two countable sets i

1) a) Prove that the union of two countable sets is countable. b) Prove that the union...

60.1K

Verified Solution

Question

Advance Math

1) a) Prove that the union of two countable sets iscountable.

b) Prove that the union of a finite collection of countable setsis countable.

Answer & Explanation Solved by verified expert
4.2 Ratings (719 Votes)
a Let A and B be countable sets We will consider four cases case 1 Suppose both A and B are finite Then A B is finite and hence countable case 2 Suppose one of A and B is finite and the other is countably infinite Assume without loss of generality that A is finite Since B is countably infinite there exists a function f B 7 Z which is a    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Biology
1.2K views

Do a search online or look in your textbook for 1-2 antibiotics that affect Gram-positive bacteria...

Advance Math
1.2K views

In each of the following, show that ? is a subgroup of ?. (1) 1. ? =...

Physics
1.2K views

Q25 A 1 0 m long wire carrying a steady current of 1 56 A...

Physics
1.2K views

A block of mass m = 3.20 kg is pushed a distance d = 5.70...

Geometry
1.2K views

What is the measure of the angle of one slice of pizza if the length...

Basic Math
1.2K views

Write the following rate as a unit rate.68 miles to 4 hours

Statistics
1.2K views

Provide an appropriate response One thousand tickets are sold at 2 each One ticket will...

Accounting
1.2K views

El 31 de diciembre, Baxtor, Inc. tiene un costo de ventas de $310 000, el...

Accounting
1.2K views

Stark Chemical Company's production process for two of its solvents can be diagrammed as follows:...

Finance
1.2K views

A company with a target D/E ratio of 0.85 has reported earnings of $925,000 for...

Accounting
1.2K views

Beginning inventory, purchases, and sales data for tennis rackets are as follows: April 3 Inventory...

Finance
1.2K views

A hypothetical futures contract on a non-dividend paying stock with a current spot price of...