What is sum?

Sum

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:

Euclid's Theorem - Euler's Proof
... To show the second 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 ... The sum on the right is the harmonic series, which diverges ...
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 ...
Jensen's Device - Description
... A classic example of Jensen's 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 ... 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 ...
Simple File Verification - Checksum
... 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, meaning ...
Characterization of Practical Numbers
... if and, for every i from 2 to k, where denotes the sum of the divisors of x ... 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 ...

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 quantity obtained by addition.
    Synonyms: amount, 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:

    The history of literature—take the net result of Tiraboshi, Warton, or Schlegel,—is a sum of a very few ideas, and of very few original tales,—all the rest being variation of these.
    Ralph Waldo Emerson (1803–1882)

    Lest darkness fall and time fall
    In a long night when learned arteries
    Mounting the ice and sum of barbarous time
    Shall yield, without essence, perfect accident.
    We are the eyelids of defeated caves.
    Allen Tate (1899–1979)

    No, the five hundred was the sum they named
    To pay the doctor’s bill and tide me over.
    It’s that or fight, and I don’t want to fight
    I just want to get settled in my life....
    Robert Frost (1874–1963)