Union of Family/Examples
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Examples of Unions of Families
Example: $\size {y - 1} < n$ and $\size {y+1} > \dfrac 1 n$
Let $I$ be the indexing set $I = \set {1, 2, 3, \ldots}$
Let $\family {T_n}$ be the indexed family of subsets of the set of real numbers $\R$, defined as:
- $T_n = \set {y: \size {y - 1} < n \land \size {y + 1} > \dfrac 1 n}$
Then:
- $\ds \bigcup_{n \mathop \in I} T_n = \R \setminus \set {-1}$