# sum

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## sum

^{1}

**1.**

**a.**the result of the addition of numbers, quantities, objects, etc.

**b.**the cardinality of the union of disjoint sets whose cardinalities are the given numbers

**2.**one or more columns or rows of numbers to be added, subtracted, multiplied, or divided

**3.**

*Maths*the limit of a series of sums of the first

*n*terms of a converging infinite series as

*n*tends to infinity

**4.**another name for number work

## sum

^{2}

## Sum’

the name used in Russian chronicles to refer to the Balto-Finnish Suomi tribe, which settled on the southwest coast of Finland early in the first millennium A.D. After subjugating the Sum’ in the mid-12th century, the Swedish feudal lords began the conquest of Finland. Subsequently, the Sum’, Häme, and western Karelian tribes combined to form the Finnish nationality.

## Sum

the result of the addition of such quantities as numbers, functions, vectors, or matrices. In all cases the commutative and associative laws hold; moreover, if multiplication is defined for the quantities in question, then it is distributive over addition. Thus, the following relations are satisfied:

*a + b = b + a*

*a + (b + c) = (a + b) + c*

*(a + b)c = ac + bc*

*c(a + b) = ca + cb*

In set theory, the sum, or union, of sets is the set whose elements belong to at least one of the given sets.

## sum

[səm]*A*+

*B*of two matrices

*A*and

*B*, with the same number of rows and columns, is the matrix whose element

*c*

_{ij }in row

*i*and column

*j*is the sum of corresponding elements

*a*

_{ij }in

*A*and

*b*

_{ij }in

*B*.

## sum

(theory)inA : A -> A+B inB : B -> A+B inA(a) = (0,a) inB(b) = (1,b)

and a disassembly operation:

case d of

**isA**

This can be generalised to arbitrary numbers of domains.

See also smash sum, disjoint union.

## sum

(tool)Unix manual page: sum(1).