Union

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Definition

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

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