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:
... 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 ak comment k and ak are passed by name begin real s s ... For 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 ...
... authenticity 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 ...
... and only if and, for every i from 2 to k, where denotes the sum of the divisors of x ... is clearly necessary in order to be able to represent as a sum of divisors of n ... the condition above, then any can be represented as a sum of divisors of n, by the following sequence of steps Let, and let ...
... 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 ...
... 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 basic unit of money in Uzbekistan.
- (verb): Determine the sum of.
Synonyms: total, tot, tot up, sum up, summate, tote up, add, add together, tally, add up
- (noun): The final aggregate.
Example: "The sum of all our troubles did not equal the misery they suffered"
Synonyms: summation, sum total
- (noun): The choicest or most essential or most vital part of some idea or experience.
Synonyms: kernel, substance, core, center, essence, gist, heart, heart and soul, inwardness, marrow, meat, nub, pith, nitty-gritty
- (noun): A quantity of money.
Example: "He borrowed a large sum"
Synonyms: sum of money, amount, amount of money
Famous quotes containing the word sum:
“And what is the potential man, after all? Is he not the sum of all that is human? Divine, in other words?”
—Henry Miller (18911980)
“To die proudly when it is no longer possible to live proudly. Death freely chosen, death at the right time, brightly and cheerfully accomplished amid children and witnesses: then a real farewell is still possible, as the one who is taking leave is still there; also a real estimate of what one has wished, drawing the sum of ones lifeall in opposition to the wretched and revolting comedy that Christianity has made of the hour of death.”
—Friedrich Nietzsche (18441900)
“Genius is no more than childhood recaptured at will, childhood equipped now with mans physical means to express itself, and with the analytical mind that enables it to bring order into the sum of experience, involuntarily amassed.”
—Charles Baudelaire (18211867)