Mapping/Examples/Area and Circumference of Circle

Examples of Mappings
Let $A$ denote the set of circles.

Let $f_1: A \to \R$ be the mapping defined on $A$ as:
 * $\forall a \in A: \map {f_1} a = \map {\Area} a$

Let $f_2: A \to \R$ be the mapping defined on $A$ as:
 * $\forall a \in A: \map {f_2} a = \map {\operatorname {Circ} } a$

where $\map {\operatorname {Circ} } a$ denotes the circumference of $a$.