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]?