Bound Variable/Examples/Family of Sets
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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 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.
Sources
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 4$: Indexed Families of Sets