Bound Variable/Examples/Family of Sets

Example of Bound Variable
Let $I$ be an indexing set.

Consider the union of the indexed family of sets $\family {S_i}_{i \mathop \in I}$:


 * $\ds \bigcup_{i \mathop \in I} S_i$

The variable $i$ is a bound variable, or dummy variable, such that $\ds \bigcup_{i \mathop \in I} S_i$ could as well be written $\ds \bigcup_{\alpha \mathop \in I} S_\alpha$ or $\ds \bigcup_{\gamma \mathop \in I} S_\gamma$, for example.