Definition:Domain (Relation Theory)/Mapping

Definition
Let $f: S \to T$ be a mapping.

The domain of $f$ is the set $S$ and can be denoted $\Dom f$.

In the context of mappings, the domain and the preimage of a mapping are the same set.

This definition is the same as that for the domain of a function.

Also known as
The domain of (usually) a mapping is called by some sources, for example, the departure set.

Others refer to it on occasion as the source, but this is not recommended as there are other uses for that term.

, for example, possibly forgetting themselves, in Appendix $\text{A}.7$:


 * Here are some common functions and their inverses. Note how carefully the source and codomain are specified.

Some sources denote the domain of $f$ by $\operatorname D \paren f$.

Also see

 * Definition:Codomain of Mapping
 * Definition:Range


 * Definition:Image of Mapping
 * Definition:Preimage of Mapping