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 ?
He was an old bachelor, and possessed of great wealth, in addition to the house and real estate which constituted what remained of the ancient Pyncheon property.
His appearance, therefore, is apt to occasion some little stir at the tea-table of a farmhouse, and the addition of a supernumerary dish of cakes or sweetmeats, or, peradventure, the parade of a silver teapot.
In addition to the pain of separation, there was the horrid dread of falling into the hands of Master Andrew.
Weston had, of course, formed a very favourable idea of the young man; and such a pleasing attention was an irresistible proof of his great good sense, and a most welcome addition to every source and every expression of congratulation which her marriage had already secured.
If he should have a numerous family, for instance, it would be a very convenient addition.
His stock consisted of a wooden stool, made out of a broken-backed chair cut down, which stool, young Jerry, walking at his father's side, carried every morning to beneath the banking-house window that was nearest Temple Bar: where, with the addition of the first handful of straw that could be gleaned from any passing vehicle to keep the cold and wet from the odd-job-man's feet, it formed the encampment for the day.
I had been taught all that others learned there; and not contented with the sciences actually taught us, I had, in addition, read all the books that had fallen into my hands, treating of such branches as are esteemed the most curious and rare.
If, in addition to the consideration of a plurality of civil lists, we take into view the number of persons who must necessarily be employed to guard the inland communication between the different confederacies against illicit trade, and who in time will infallibly spring up out of the necessities of revenue; and if we also take into view the military establishments which it has been shown would unavoidably result from the jealousies and conflicts of the several nations into which the States would be divided, we shall clearly discover that a separation would be not less injurious to the economy, than to the tranquillity, commerce, revenue, and liberty of every part.
If the new Constitution be examined with accuracy and candor, it will be found that the change which it proposes consists much less in the addition of NEW POWERS to the Union, than in the invigoration of its ORIGINAL POWERS.
In addition, Ogilvy's wire to the Astronomical Exchange had roused every observatory in the three kingdoms.
I often feel as he did, dearest, and, in addition, I know how beholden to you I am.
As soon as all had ate, and the elder ones paid, the carriage was ordered; and after some contrivance, the whole party, with all their boxes, work-bags, and parcels, and the unwelcome addition of Kitty's and Lydia's purchases, were seated in it.