Union of Family/Examples

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:

$\ds \bigcup_{n \mathop \in I} T_n = \R \setminus \set {-1}$