# 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 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

**vector,**

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 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

*a*

**.....**Click the link for more information. .

The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/

## Addition

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

Illustrated Dictionary of Architecture Copyright © 2012, 2002, 1998 by The McGraw-Hill Companies, Inc. All rights reserved

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## 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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

## 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.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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).

McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.

## addition

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

**+**Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005