Sum word meaning and definition

[noun] the whole amount
[noun] a quantity obtained by addition
[noun] the choicest or most essential or most vital part of some idea or experience; "the gist of the prosecutor's argument"; "the heart and soul of the Republican Party"; "the nub of the story"
[noun] a set containing all and only the members of two or more given sets; "let C be the union of the sets A and B"
[noun] the final aggregate; "the sum of all our troubles did not equal the misery they suffered"
[noun] a quantity of money; "he borrowed a large sum"; "the amount he had in cash was insufficient"
[verb] determine the sum of; "Add all the people in this town to those of the neighboring town"
[verb] be a summary of; "The abstract summarizes the main ideas in the paper"

\Sum\, n. [OE. summe, somme, OF. sume, some, F. somme, L. summa, fr. summus highest, a superlative from sub under. See {Sub-}, and cf. {Supreme}.] 1. The aggregate of two or more numbers, magnitudes, quantities, or particulars; the amount or whole of any number of individuals or particulars added together; as, the sum of 5 and 7 is 12. Take ye the sum of all the congregation. --Num. i. 2. Note: Sum is now commonly applied to an aggregate of numbers, and number to an aggregate of persons or things. 2. A quantity of money or currency; any amount, indefinitely; as, a sum of money; a small sum, or a large sum. ``The sum of forty pound.'' --Chaucer. With a great sum obtained I this freedom. --Acts xxii. 28. 3. The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections. 4. Height; completion; utmost degree. Thus have I told thee all my state, and brought My story to the sum of earthly bliss. --Milton. 5. (Arith.) A problem to be solved, or an example to be wrought out. --Macaulay. A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole. --Gladstone. A large sheet of paper . . . covered with long sums. --Dickens. {Algebraic sum}, as distinguished from arithmetical sum, the aggregate of two or more numbers or quantities taken with regard to their signs, as + or -, according to the rules of addition in algebra; thus, the algebraic sum of -2, 8, and -1 is 5. {In sum}, in short; in brief. [Obs.] ``In sum, the gospel . . . prescribes every virtue to our conduct, and forbids every sin.'' --Rogers.
\Sum\, v. t. [imp. & p. p. {Summed}; p. pr. & vb. n. {Summing}.] [Cf. F. sommer, LL. summare.] 1. To bring together into one whole; to collect into one amount; to cast up, as a column of figures; to ascertain the totality of; -- usually with up. The mind doth value every moment, and then the hour doth rather sum up the moments, than divide the day. --Bacon. 2. To bring or collect into a small compass; to comprise in a few words; to condense; -- usually with up. ``Go to the ant, thou sluggard,'' in few words sums up the moral of this fable. --L'Estrange. He sums their virtues in himself alone. --Dryden. 3. (Falconry) To have (the feathers) full grown; to furnish with complete, or full-grown, plumage. But feathered soon and fledge They summed their pens [wings]. --Milton. {Summing up}, a compendium or abridgment; a recapitulation; a r['e]sum['e]; a summary. Syn: To cast up; collect; comprise; condense; comprehend; compute.
inA : A -> A+B inB : B -> A+B inA
(a) = (0,a) inB
(b) = (1,b)

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