# 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 ... The sum on the right is the harmonic series, which diverges ...
Simple File Verification - Checksum
... 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 ...
Characterization of Practical Numbers
... if and only if and, for every i from 2 to k, where denotes the sum of the divisors of x ... In one direction, this condition is 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
... 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 ak comment k and ak are passed by name begin real s s = 0 for k = l ... 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 ...
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 ...

### 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): The basic unit of money in Uzbekistan.
• (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

### Famous quotes containing the word sum:

The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.
Anton Pavlovich Chekhov (1860–1904)

I would sum up my fear about the future in one word: boring. And that’s my one fear: that everything has happened; nothing exciting or new or interesting is ever going to happen again ... the future is just going to be a vast, conforming suburb of the soul.
—J.G. (James Graham)

Society does not consist of individuals but expresses the sum of interrelations, the relations within which these individuals stand.
Karl Marx (1818–1883)