Totality

A function from set $X$ to set $Y$, noted as $f : X \to Y$, is total if the domain for which $f$ is defined is equal to $X$. On the contrary, if $f$ is not defined for some element in $X$, then $f$ is said to be a partial function.

Remarks

When a function is not specified as a partial function, it is implicitly a total function.