Algebraic sum

Sum 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. [1913 Webster]

Take ye the sum of all the congregation. --Num. i. 2. [1913 Webster]

Note: Sum is now commonly applied to an aggregate of numbers, and number to an aggregate of persons or things. [1913 Webster]

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. [1913 Webster]

With a great sum obtained I this freedom. --Acts xxii. 28. [1913 Webster]

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. [1913 Webster]

4. Height; completion; utmost degree. [1913 Webster]

Thus have I told thee all my state, and brought My story to the sum of earthly bliss. --Milton. [1913 Webster]

5. (Arith.) A problem to be solved, or an example to be wrought out. --Macaulay. [1913 Webster]

A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole. --Gladstone. [1913 Webster]

A large sheet of paper . . . covered with long sums. --Dickens. [1913 Webster]

{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. [1913 Webster]