• Support PF! Buy your school textbooks, materials and every day products Here!

Cardinality Question from Basic Analysis. Thanks for any help.

  • #1

Homework Statement


If the cardinality of A is less than or equal to the cardinality of the reals and the cardinality of B is less than or equal to the cardinality of the reals, I need to show that the cardinality of the union of A and B is less than or equal to the cardinality of the reals.

IE: Prove that if |A|</=|R| and |B|</=|R|, then |AUB|</=|R|.

Thanks for any help. I am in a basic analysis class, and we just started a small section on cardinality.


Homework Equations





The Attempt at a Solution


All I know is that based on my assumption, I know that there is a 1-1 function from A to the real numbers and another 1-1 function from B to the real numbers.
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
19
Have you learned anything about the arithmetic of cardinal numbers?
 
  • #3
Nope, sorry.
 

Related Threads on Cardinality Question from Basic Analysis. Thanks for any help.

Replies
23
Views
2K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
8
Views
2K
Replies
1
Views
6K
Replies
5
Views
1K
  • Last Post
Replies
1
Views
776
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
Top