domain

The term domain has (at least) three different meanings in mathematics .

See https://mathworld.wolfram.com/Domain.html
This note refers to the most common one.

Domain of a function

If $f:A\to B$ is a function from set $A$ to set $B$, then the domain of $f$ is the set $A$.

“A function over A”

$f(x)=x^2$

The domain of $f$ is $\mathbb{R}$, the set of all real numbers.

“Definitionsmenge”