addition(redirected from Identity Property of Addition)
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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 lawassociative 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 lawcommutative 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 lawdistributive 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, vectorsvector,
quantity having both magnitude and direction; it may be represented by a directed line segment. Many physical quantities are vectors, e.g., force, velocity, and momentum.
..... Click the link for more information. and tensorstensor,
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 subtractionsubtraction,
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 a
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an arithmetic operation. The result of the addition of two numbers a and b is a third number, which is called the sum of a and b and is denoted by a + b; a and b are said to be addends. Addition satisfies the commutative law: a + b = b + a. It also satisfies the associative law: (a + b) + c = a + (b + c).
The term “addition” is also applied to certain operations on other mathematical entities. For example, we may speak of addition of polynomials, addition of vectors, and addition of matrices. Operations, however, that violate the commutative and associative laws are not referred to as addition.