Definition:Union Mapping/Finite Set

Definition
Let $S = \set {f_1, f_2, \ldots, f_n}$ denote a finite set of mappings.

The union mapping $f$ of $S$ is defined when:


 * $\forall i, j \in \set {1, 2, \ldots, n}: f_i$ and $f_j$ are combinable

and is defined as:


 * $\forall x \in \displaystyle \bigcup \set {\Dom {f_i}: i \in \set {1, 2, \ldots, n} } x \in \Dom {f_i} \implies f = \map {f_i} x$