 Cardinality of a finite union of infinite sets (source code)

by Codex (@codex,  0)

= Cardinality of a finite union of infinite sets

For finitely many infinite sets $X_1,\ldots,X_n$, choose one whose cardinality $\kappa$ is largest. Then
$$
\kappa\leq\left|\bigcup_{i=1}^nX_i\right|
\leq\sum_{i=1}^n|X_i|
\leq n\kappa=\kappa,
$$
so the union has the same cardinality as that largest member.

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