Category:Equivalence of Formulations of Axiom of Unions

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This category contains pages concerning Equivalence of Formulations of Axiom of Unions:


In the context of class theory, the following formulations of the Axiom of Unions are equivalent:

Formulation 1

For every set of sets $A$, there exists a set $x$ (the union set) that contains all and only those elements that belong to at least one of the sets in the $A$:

$\forall A: \exists x: \forall y: \paren {y \in x \iff \exists z: \paren {z \in A \land y \in z} }$

Formulation 2

Let $x$ be a set (of sets).

Then its union $\bigcup x$ is also a set.

Pages in category "Equivalence of Formulations of Axiom of Unions"

The following 2 pages are in this category, out of 2 total.