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

Counting infinite sequence of sets

  • #1
Let K1, K2, K3, . . . be an infnite sequence of sets, where each set Kn is countable.
Prove that the union of all of these sets K = Union from n=1 to infinity, Kn is countable.

I tried to start, but I don't even understand the question

Need some idea on how to start
 
Last edited:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Not understanding the question is not a good start. What does 'countable' mean?
 
  • #3
Denumerable?

The set K would be denumberable if there is a bijection ZZ+->K

by the way, can you teach me how to read "Bijection ZZ+->K?" ZZ+ is the symbol for all positive integer, -> is the arrow pointing to the set K.
and I have trouble understanding what F: NN -> A mean intuitively
 
Last edited:
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
I don't know what you are talking about. What does ZZ+->X mean? Countable means there is a bijection with N, the natural numbers. This is basically the same proof as showing NxN is countable. How do you do that?
 
  • #5
I'm sorry, >.< but what does NxN mean? is it the symbol for natural number?
 

Related Threads on Counting infinite sequence of sets

  • Last Post
Replies
0
Views
720
Replies
3
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
9
Views
7K
Replies
3
Views
10K
  • Last Post
Replies
6
Views
6K
  • Last Post
Replies
2
Views
551
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
2
Views
4K
Top