Union

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Definition

Given a collection of sets $\{S_\alpha\}_{\alpha\in A}$ their union is:

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