Does the following function
$f:\mathcal{P}(\mathbb{N})\rightarrow{0,1}$ f:\mathcal{P}(\mathbb{N})\rightarrow\{0,1\}$ exist :
$f(\mathbb{N})=1$,
$f(A\cup B)=f(A)+f(B)$ for $A\cap B=\emptyset$,
$f(A)=0$ for finite $A$
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Existence of a special densityDoes the following function
$f:\mathcal{P}(\mathbb{N})\rightarrow{0,1}$ exist :
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