The domain $~$\operatorname{dom}(f)$~$ of a function $~$f : X \to Y$~$ is $~$X$~$, the set of valid inputs for that function. For example, the domain of $~$+$~$ is the set of all pairs of numbers, and the domain of the division operation is the set of all pairs $~$(x, y)$~$ of numbers where $~$y$~$ is non-zero.
Visualizing a function as a map that takes every point in an input set to one point in an output set, the domain is the input set (pictured on the left in red in the image below).
