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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Famous quotes containing the word sum:

    “[M]y conception of liberty does not permit an individual citizen or a group of citizens to commit acts of depredation against nature in such a way as to harm their neighbors and especially to harm the future generations of Americans. If many years ago we had had the necessary knowledge, and especially the necessary willingness on the part of the Federal Government, we would have saved a sum, a sum of money which has cost the taxpayers of America two billion dollars.”
    —Franklin D. Roosevelt (1882–1945)

    “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 one’s life—all in opposition to the wretched and revolting comedy that Christianity has made of the hour of death.”
    —Friedrich Nietzsche (1844–1900)

    “The real risks for any artist are taken ... in pushing the work to the limits of what is possible, in the attempt to increase the sum of what it is possible to think. Books become good when they go to this edge and risk falling over it—when they endanger the artist by reason of what he has, or has not, artistically dared.”
    —Salman Rushdie (b. 1947)