Counting infinite sequence of sets

[ihatewonders]

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

 

[Dick]

Not understanding the question is not a good start. What does 'countable' mean?

 

[ihatewonders]

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

 

[Dick]

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?

 

[ihatewonders]

I'm sorry, >.< but what does NxN mean? is it the symbol for natural number?