Definition:Limit of Increasing Sequence of Sets

Definition
Let $\sequence {S_n}_{n \mathop \in \N}$ be an increasing sequence of sets.

Let $S = \ds \bigcup_{n \mathop \in \N} S_n$.

Then $S$ is said to be the limit of $\sequence {S_n}_{n \mathop \in \N}$, and one writes $S_n \uparrow S$.

Also see

 * Limit of Decreasing Sequence of Sets
 * Increasing Sequence of Sets