addition

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ad·di·tion / əˈdishən/ (abbr.: addn.) • n. 1. the action or process of adding something to something else: the hotel has been extended with the addition of more rooms. ∎  a person or thing added or joined, typically in order to improve something: you will find the coat a useful addition to your wardrobe. 2. (abbr.: addn.) the process or skill of calculating the total of two or more numbers or amounts. ∎  Math. the process of combining matrices, vectors, or other quantities under specific rules to obtain their sum. PHRASES: in addition as an extra person, thing, or circumstance: members of the board were paid a small allowance in addition to their salary.

addition fundamental operation of arithmetic, denoted by +. In counting, a + b represents the number of items in the union of two collections having no common members (disjoint sets), having respectively a and b members. In geometry a + b might, for example, represent the area of the union of two disjoint regions of areas a and b, respectively. In arithmetic addition follows the associative law , the commutative law , and, in combination with multiplication, the distributive law . Addition is also defined for other types of mathematical objects, for example, vectors and tensors . See also subtraction .

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