# 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 +
References in classic literature ?
In addition to this, I gave private lessons to several young men whom I was fitting to send to the Hampton Institute.
In addition to matters treated in the text, consider how much feeling the authors show for Nature, and their power of description.
Some, in addition to those above stated, are: How far is it a mere Chronicle-history play, how far a regular tragedy?
In addition to those above suggested, the character of Hamlet is an attractive topic.
She was to be their chosen visitor, she was to be for weeks under the same roof with the person whose society she mostly prized -- and, in addition to all the rest, this roof was to be the roof of an abbey
On the whole his surmises, in addition to what he knew of the fact, increased his friendliness and tolerance towards Ladislaw, and made him understand the vacillation which kept him at Middlemarch after he had said that he should go away.
One would think that this was enough for one day, but Mynheer Boxtel did not seem to think so, as, in addition to having his clothes torn, his back bruised, and his hands scratched, he inflicted upon himself the further punishment of tearing out his hair by handfuls, as an offering to that goddess of envy who, as mythology teaches us, wears a head-dress of serpents.
In addition to Web browser access for internal Web applications and file servers, INS consultants get full VPN application access with additional network and desktop protection by using Aventail Connect, a Web-delivered Windows agent.
Often overlooked in the hype about criminals is the fact that all the deportees have already served their sentences in state or local prisons, in addition to being held in indefinite INS detention.

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