(A consequence of this is that an additive function cannot take both and + as values, for the expression is undefined.)

One may define additive functions with values in any additive monoid (for example any group or more commonly a vector space).

Because of local independence, item information functions are additive function.

The remainder of this article discusses number theoretic additive functions, using the second definition.

Every completely additive function is additive, but not vice versa.

Solutions to this are called additive functions.

But education is not an additive function.

In particular, the values of additive and multiplicative functions are determined by their values on the powers of prime numbers.

This proved to be an additive function of atomic constants with structural constants in addition.

The logarithmic derivative is a totally additive function.