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Proof: (related to "Justification of Set Union")

  • Let $A$ and $B$ be sets.

  • By the axiom of pairing there is a set $Z$ containing $A$ and $B$ as elements:

  • By the axiom of union there is a set $Z^*$ containing the elements of $A$ or1 the elements of $B.$

  • By the axiom of separation there is a subset $Z^\dagger \subseteq Z^*$ containing exactly the elements of $A$ or1 the elements of $B.$, i.e. $Z^\dagger =\{z\mid z\in A\vee z\in B\}.$

1 We mean the logical or operation, in the natural English language “and/or”.

q.e.d

| | | | Contributors: bookofproofs | References: [983]


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Bibliography (further reading)

[983] Ebbinghaus, H.-D.: “Einf├╝hrung in die Mengenlehre”, BI Wisschenschaftsverlag, 1994, 3

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