# Cardinality is Additive Function

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## Theorem

Let $S$ be a finite set.

Let $\powerset S$ be the power set of $S$.

The function $C: \powerset S \to \R$, where $C$ is defined as the cardinality of a set, is an additive function.

## Proof

We have that $\powerset S$ is an algebra of sets.

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