In mathematics, the indicator vector, characteristic vector, or incidence vector of a subset T of a set S is the vector such that if and if
If S is countable and its elements are numbered so that , then where if and if
To put it more simply, the indicator vector of T is a vector with one element for each element in S, with that element being one if the corresponding element of S is in T, and zero if it is not.
An indicator vector is a special (countable) case of an indicator function.
If S is the set of natural numbers , and T is some subset of the natural numbers, then the indicator vector is naturally a single point in the Cantor space: that is, an infinite sequence of 1's and 0's, indicating membership, or lack thereof, in T. Such vectors commonly occur in the study of arithmetical hierarchy.