domain (function)

For a function $f\subseteq A\times B$, the set $A$ is the domain. All values of $A$ must be valid arguments of $f$; for instance, the function $f(x)=\frac{1}{x}$ can be represented as $f:\mathbb{R}-\{0\}\to \mathbb{R}$. $f(x)=\frac{1}{x}$ can also be described as a partial function from $\mathbb{R}$ to $\mathbb{R}$ since its domain is a subset of $\mathbb{R}$.