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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Famous quotes containing the word sum:
“Looking foolish does the spirit good. The need not to look foolish is one of youth’s many burdens; as we get older we are exempted from more and more, and float upward in our heedlessness, singing Gratia Dei sum quod sum.”
—John Updike (b. 1932)
“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)
“If the twentieth century is to be better than the nineteenth, it will be because there are among us men who walk in Priestley’s footsteps....To all eternity, the sum of truth and right will have been increased by their means; to all eternity, falsehoods and injustice will be the weaker because they have lived.”
—Thomas Henry Huxley (1825–95)