addition definition of addition in the Free Online Encyclopedia.

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 associative law, in mathematics, law holding that for a given operation combining three quantities, two at a time, the initial pairing is arbitrary; e.g., using the operation of addition, the numbers 2, 3, and 4 may be combined (2+3)+4=5+4=9 or 2+(3+4)=2+7=9.
..... Click the link for more information. , the commutative law commutative law, in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7.
..... Click the link for more information. , and, in combination with multiplication, the distributive law distributive law. In mathematics, given any two operations, symbolized by * and +, the first operation, *, is distributive over the second, +, if a*(b+c)=(a*b)+(a*c) for all possible choices of a, b, and c.
..... Click the link for more information. . Addition is also defined for other types of mathematical objects, for example, vectors U [−3,1] and V [5,2], one can add their corresponding components to find the resultant vector R [2,3], or one can graph U and V on a set of coordinate axes and complete the parallelogram formed with U and V
..... Click the link for more information. and tensors tensor, in mathematics, quantity that depends linearly on several vector variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates ).
..... Click the link for more information. . See also subtraction subtraction, fundamental operation of arithmetic; the inverse of addition. If a and b are real numbers (see number ), then the number a−b is that number (called the difference) which when added to b (the subtractor) equals
..... Click the link for more information. .

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addition