[[Cardinality]]
# Upper bound on the cardinality of an arbitrary union

Let $\{ A_{k} \}_{k \in K}$ be a collection of sets such that $\abs{A_{k}} \leq \lambda$ for all $k \in K$ and $\abs K = \kappa$.
Then[^2008] #m/thm/set 
$$
\begin{align*}
\abs{\bigcup_{k \in K}A_{k}} \leq \lambda\kappa
\end{align*}
$$

> [!missing]- Proof
> #missing/proof 

[^2008]: 2008\. [[Sources/@romanAdvancedLinearAlgebra2008|Advanced Linear Algebra]], p. 16


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