Counting infinite sequence of sets

ihatewonders
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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?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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