Union Mapping/Examples
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Examples of Union Mappings
Absolute Value Function
Let $f_1: \R_{\ge 0} \to \R$ be the real function defined on the set of positive real numbers $\R_{\ge 0}$ as:
- $\forall x \in \R_{\ge 0}: \map {f_1} x = x$
Let $f_2: \R_{\le 0} \to \R$ be the real function defined on the set of negative real numbers $\R_{\le 0}$ as:
- $\forall x \in \R_{\le 0}: \map {f_2} x = -x$
Then:
- $f_1$ and $f_2$ are combinable mappings
and:
- the union mapping $f = f_1 \cup f_2$ is:
- $\forall x \in \R: \map f x = \size x$
- where $\size x$ denotes the absolute value of $x$.