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# Def/Union

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Definition of Union: If $X$ is a set, then $\bigcup X$ is the set whose elements are those $u$ which are elements of elements of $X$. In other words, $$x \in \bigcup X \mbox{ iff } \exists u \in X, x \in u.$$

The set $\bigcup X$ is called the union (of the elements) of $X$.

When $X$ is an unordered pair, such as $X = \{ A, B \}$, one uses the notation $A \cup B$ to stand for $\bigcup \{A, B \}$.

## Logical Connections

This definition logically relies on the following definitions and statements: State/Axiom of unions, State/Axiom of extensionality

The following statements and definitions logically rely on the material of this page: Def/Ordinal number, Def/Successor, and State/Axiom of infinity

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Basic set theory