What is "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 1

2. 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.