The term Sum from the Latin Summa , is everything related to the addition or aggregation of quantities or things. In general, it is defined as a basic mathematical operation, which consists of gathering the units of two or more numbers, each one separately, the result of which will be another number made up of as many units as its components have.
In addition as is known the sum, the sign used is a cross (+) is called more, the quantities add called addends and the result is called sum.
This means that the word sum designates both the operation and the result of it. For example, when saying "the sum of natural numbers fulfills the associative property" , the word sum refers to the operation. When saying "the sum of 3 and 2 is 5" , the word sum means the result of the operation.
The sum is defined on sets of natural, integer, rational, real and complex numbers, and also on structures associated with them, such as vector spaces with vectors whose components are these numbers or functions that have their image in them.
Commonly, it is represented in different properties: the commutative, where the result of a sum does not depend on the order of the addends, a + b + c = c + b + a; the associative, which consists in that the addends can be grouped in arbitrary order without altering the final result, (a + b) + (c + d) = b + (a + c + d).
The dissociative is also found, in it the sum of several numbers is not altered by substituting one or more addends so that the sum of the new components is equal to the first, b = m + n -> a + b + c = a + (m + n) + c; and finally, existence of the neutral element, where the sum of any quantity with the neutral element will have the same quantity as a result. In addition, the neutral element is the number zero (0).
On the other hand, the sum is also considered as the compendium, compilation or summary of all the parts of a science or faculty; it is, generally, the knowledge of knowledge. For example: Maria compiled a complete sum of Biology for her studies.
