Editing Addition (section)

{{Short description|Arithmetic operation}}
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{{Redirect|Add||ADD (disambiguation)}}
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[[File:Addition01.svg|right|thumb|upright=0.5|3 + 2 = 5 with [[apple]]s, a popular choice in textbooks<ref>{{harvtxt|Enderton|1977}}, p. [http://books.google.com/books?id=JlR-Ehk35XkC&pg=PA138 138]: "...select two sets ''K'' and ''L'' with card ''K'' = 2 and card ''L'' = 3. Sets of fingers are handy; sets of apples are preferred by textbooks."</ref>]]

'''Addition''' (usually signified by the [[Plus and minus signs#Plus sign|plus symbol]], +) is one of the four basic [[Operation (mathematics)|operations]] of [[arithmetic]], the other three being [[subtraction]], [[multiplication]], and [[Division (mathematics)|division]]. The addition of two [[Natural number|whole numbers]] results in the total or ''[[summation|sum]]'' of those values combined. For example, the adjacent image shows two columns of apples, one with three apples and the other with two apples, totaling to five apples. This observation is expressed as {{nowrap|1="3 + 2 = 5"}}, which is read as  "three plus two [[Equality (mathematics)|equal]]s five".

Besides [[counting]] items, addition can also be defined and executed without referring to [[concrete object]]s, using abstractions called [[number]]s instead, such as [[integer]]s, [[real number]]s, and [[complex number]]s. Addition belongs to arithmetic, a branch of [[mathematics]]. In [[algebra]], another area of mathematics, addition can also be performed on abstract objects such as [[Euclidean vector|vectors]], [[Matrix (mathematics)|matrices]], [[Linear subspace|subspaces]], and [[subgroup]]s.

Addition has several important properties. It is [[Commutative property|commutative]], meaning that the order of the [[operand|numbers being added]] does not matter, so {{nowrap|1=3 + 2 = 2 + 3}}, and it is [[associativity|associative]], meaning that when one adds more than two numbers, the order in which addition is performed does not matter. Repeated addition of {{num|1}} is the same as counting (see [[Successor function]]). Addition of {{num|0}} does not change a number. Addition also obeys rules concerning related operations such as subtraction and multiplication.

Performing addition is one of the simplest numerical tasks to perform. Addition of very small numbers is accessible to toddlers; the most basic task, {{nowrap|1 + 1}}, can be performed by infants as young as five months, and even some members of other animal species. In [[primary education]], students are taught to add numbers in the [[decimal]] system, beginning with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient [[abacus]] to the modern [[computer]], where research on the most efficient implementations of addition continues to this day.
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