# Definition:Domain (Set 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 1975: T.S. Blyth: Set Theory and Abstract Algebra, 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.

1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability, 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 $\operatorname D \paren f$.

## Technical Note

The $\LaTeX$ code for $\Dom {X}$ is \Dom {X} .

When the argument is a single character, it is usual to omit the braces:

\Dom X