# Union

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## Definition

Given a collection of sets [ilmath]\{S_\alpha\}_{\alpha\in A} [/ilmath] their union is:

• $\bigcup_{\alpha\in A}S_\alpha$ with the characteristic property that:
• $x\in\bigcup_{\alpha\in A}S_\alpha\iff\exists\beta\in A[x\in S_\beta]$