Minimum excludant ($\mathrm{mex}$)

The minimum excludant of a finite set of nonnegative integers is the smallest nonnegative integer absent from the set. For example, $\mathrm{mex}\{0,1,3\}=2$.

For a set of positive integers, its minimum excluded positive integer is the least positive integer absent from the set. This is the positive-indexed version of the minimum excludant, which normally allows zero.