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.
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, 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.
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, 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.
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. 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.
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 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).
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. See also subtractionsubtraction,
fundamental operation of arithmetic; the inverse of addition. If a and b are real numbers (see number), then the number ab is that number (called the difference) which when added to b (the subtractor) equals a
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.

Addition

Construction that increases the size of the original structure by building outside the existing walls or roof.

Addition

 

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.

addition

[ə′di·shən]
(mathematics)
An operation by which two elements of a set are combined to yield a third; denoted +; usually reserved for the operation in an Abelian group or the group operation in a ring or vector space.
The combining of complex quantities in which the individual real parts and the individual imaginary parts are separately added.
The combining of vectors in a prescribed way; for example, by algebraically adding corresponding components of vectors or by forming the third side of the triangle whose other sides each represent a vector. Also known as composition.

addition

1. A floor or floors, a room, wing, or other expansion to an existing building.
2. In building code usage: Any new construction which increases the height or floor area of an existing building or adds to it (as a porch or attached garage).
3. An amount added to the contract sum by a charge order; also see extra.

addition

a mathematical operation in which the sum of two numbers or quantities is calculated. Usually indicated by the symbol +
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