> 
> Suppose our probability space $W$ is the set $\mathbb{N} = \{0,1,2,\dots\}$ of natural numbers, and $\mathcal{A}$ is the algebra of all subsets of $\mathbb{N}$.
>  Suppose we define a function $P$ on $\mathcal{A}$ such that $P(X) = 0$ whenever $X\in\mathcal{A}$ is finite, and $P(X) = 1$ when $X$ is infinite.
>  Is $P$ finitely additive?
>  Either prove it is, or explain why it is not.
> 
> 
> 

Where do I start with this proof? I'm new to probability, and could use a solid hint.