What is sum?

  • (noun): A quantity obtained by addition.
    Synonyms: amount, total
    See also — Additional definitions below


Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid). For finite sequences of such elements, summation always produces a well-defined sum (possibly by virtue of the convention for empty sums).

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Some articles on sum:

Residual Sum Of Squares
... In statistics, the residual sum of squares (RSS) is the sum of squares of residuals ... It is also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE) ... In general, total sum of squares = explained sum of squares + residual sum of squares ...
Characterization of Practical Numbers
... every i from 2 to k, where denotes the sum of the divisors of x ... clearly necessary in order to be able to represent as a sum of divisors of n ... the factorization of n satisfies the condition above, then any can be represented as a sum of divisors of n, by the following sequence of steps Let, and let ...
Jensen's Device - Description
... device is a procedure that computes the sum of a series, real procedure Sum(k, l, u, ak) value l, u integer k, l, u real ak comment k and ak are passed by name ... example, code to compute the first 100 terms of a real array V would be Sum(i, 1, 100, V) ... During the execution of Sum, the actual argument i will increment during each step of the for loop, and each of the procedure's evaluations of ak will use the current value of i to access the successive array ...
Simple File Verification - Checksum
... of files, as CRC32 is not a collision resistant hash function even if the hash sum file is not tampered with, it is computationally trivial for an attacker to cause deliberate hash collisions ...
Euclid's Theorem - Euler's Proof
... equality, distribute the product over the sum in the result, every product of primes appears exactly once, so by the fundamental theorem of arithmetic, the sum is equal to the sum over all integers ... The sum on the right is the harmonic series, which diverges ...

More definitions of "sum":

  • (noun): The final aggregate.
    Example: "The sum of all our troubles did not equal the misery they suffered"
    Synonyms: summation, sum total
  • (noun): A set containing all and only the members of two or more given sets.
    Synonyms: union, join
  • (noun): The basic unit of money in Uzbekistan.

Famous quotes containing the word sum:

    I was brought up to believe that the only thing worth doing was to add to the sum of accurate information in the world.
    Margaret Mead (1901–1978)

    To help, to continually help and share, that is the sum of all knowledge; that is the meaning of art.
    Eleonora Duse (1859–1924)

    The sum and substance of female education in America, as in England, is training women to consider marriage as the sole object in life, and to pretend that they do not think so.
    Harriet Martineau (1802–1876)