Support ($\mathrm{supp}f$)

The support of a function is the closure of the set on which it is nonzero.

If two functions are zero outside finite supports and a binary operation satisfies $F(0,0)=0$, the pointwise result is zero outside the union of those supports. Enumerating their union is therefore sufficient for addition, subtraction, maximum and minimum of signed count functions. It is also sufficient to test their pointwise order, since $0\le 0$ elsewhere. Neither scanning only the left support nor intersecting supports is generally valid when negative values are allowed.

A function has compact support when its support is a compact set.