sum

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

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sum

²

the standard monetary unit of Uzbekistan, divided into 100 tiyin

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.

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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]

(mathematics)

The addition of numbers or mathematical objects in context.

The sum of an infinite series is the limit of the sequence consisting of all partial sums of the series.

The sum 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)

In domain theory, the sum A + B of two domains contains all elements of both domains, modified to indicate which part of the union they come from, plus a new bottom element. There are two constructor functions associated with the sum:

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)

A Unix utility to calculate a 16-bit checksum of the data in a file. It also displays the size of the file, either in kilobytes or in 512-byte blocks. The checksum may differ on machines with 16-bit and 32-bit ints.

Unix manual page: sum(1).