Subtraction

Subtraction is the mathematical function which involves the decrease of a value, the minuend, by another value, the subtrahend, which yields a directly related linear decrease in the overall value, except in the case of a negative subtrahend, in which case the value increases.

Subtraction as Negative Addition

One problem with subtraction is that is non-commutative, which excludes the operation from being considered in an abelian group. One way to circumvent this is to view all subtraction operations as additions of the negative. For example, 5 - 1 = 4 can not be commuted, as 1 - 5 = -4. However, if this equation is viewed a negative addition, i.e. 5 + (-1) = 4, it maintains commutativity, since (-1) + 5 = 4.