negativesum

Negativesum is a term used in mathematics and computer science to denote the additive inverse of the sum of a collection of numbers or values. Formally, for a finite sequence a1, a2, ..., an, negativesum(a1, a2, ..., an) = -(a1 + a2 + ... + an). It is often written as -sum(a1, a2, ..., an) or described as the negative of the total.

In mathematical terms, negativesum acts as the negative of a total: if you sum a set of numbers and then take the additive inverse, you obtain the negativesum. If the input sum is S, then negativesum equals -S. When S is zero, the negativesum is also zero. The concept generalizes to lists, arrays, or multisets of numbers and aligns with the idea that the negative of a sum equals the sum of the negatives: - (a1 + a2 + ... + an) = (-a1) + (-a2) + ... + (-an).

In programming, negativesum is commonly implemented as a function that takes a sequence of numbers and returns the negated total, often simply as return -sum(numbers). It is distinct in wording from the sum of negatives, which is the sum of the negated elements and yields the same result for real numbers.

Applications of the negativesum concept appear in algebraic manipulation, algorithm design, and numerical methods where controlling the sign of a total is useful. It relies on the existence of additive inverses in the underlying number system, such as the real numbers or integers. See also sum, additive inverse, and zero-sum concepts for related ideas.