Counting infinite sequence of sets

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The discussion revolves around proving that the union of an infinite sequence of countable sets is also countable. Participants express confusion about the concept of countability and the notation used, such as bijections and the symbols ZZ+ and NxN. It is clarified that countable sets can be put into a one-to-one correspondence with the natural numbers. The proof involves demonstrating that a union of countable sets can be indexed similarly to the Cartesian product of natural numbers. Understanding these concepts is crucial for tackling the problem effectively.
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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
 
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Not understanding the question is not a good start. What does 'countable' mean?
 
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
 
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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?
 
I'm sorry, >.< but what does NxN mean? is it the symbol for natural number?
 

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