Is coutnable unions of finite sets an infinite set? (1 Viewer)

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Hiya. :)

While doing an assignment I ran into this little problem.

We are working in the set of natural numbers [tex]\mathbb{N}[/tex].

If i collect each natural number in a set
[tex]S_1 = \{1\}, S_2 = \{2\},\ldots, S_n = \{n\},\ldots[/tex]

What happens when I take the countable union of all these?
[tex]S = \bigcup_{i\in\mathbb{N}}S_i[/tex]

The resulting set will be an infinite set, right? It will be equal to [tex]\mathbb{N}[/tex]?
 

CRGreathouse

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Yup.

Finite unions of finite sets are finite.

Countable unions of finite sets are countable.

Finite unions of countable sets are countable.

Countable unions of countable sets are countable.
 
Thanks.

I was just really unsure there for a moment, but I think I see it now.
Thanks for clearing that up for me.

PS Sorry about the typo in the thread title.
 

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