AskDefine | Define sum

Dictionary Definition



1 a quantity of money; "he borrowed a large sum"; "the amount he had in cash was insufficient" [syn: sum of money, amount, amount of money]
2 a quantity obtained by addition [syn: amount, total]
3 the final aggregate; "the sum of all our troubles did not equal the misery they suffered" [syn: summation, sum total]
4 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" [syn: kernel, substance, core, center, essence, gist, heart, heart and soul, inwardness, marrow, meat, nub, pith, nitty-gritty]
5 the whole amount [syn: total, totality, aggregate]
6 the basic unit of money in Uzbekistan
7 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" [syn: union, join]


1 be a summary of; "The abstract summarizes the main ideas in the paper" [syn: summarize, summarise, sum up]
2 determine the sum of; "Add all the people in this town to those of the neighboring town" [syn: total, tot, tot up, sum up, summate, tote up, add, add together, tally, add up] [also: summing, summed]

User Contributed Dictionary



  • sŭm, /sʌm/, /sVm/
    Rhymes: -ʌm


Etymology 1

summe, from , from summa, feminine of summus, highest


  1. A quantity obtained by addition or aggregation.
    The sum of 3 and 4 is 7.
  2. An arithmetic computation, especially one posed to a student as an exercise (not necessarily limited to addition.)
  3. A quantity of money.
  4. A summary.
  5. A central idea or point.
  6. The utmost degree.
  7. An old English measure of corn equal to the quarter.
    • 1882, The sum is also used for the quarter, and the strike for the bushel. — James Edwin Thorold Rogers, A History of Agriculture and Prices in England, Volume 4, p. 207.
Derived terms
quantity obtained by addition or aggregation
  • Arabic:
  • Chinese: 總數, 总数 (zǒngshù)
  • Czech: součet
  • Dutch: som
  • Finnish: summa
  • French: somme
  • German: Summe
  • Greek: άθροισμα
  • Hungarian: összeg
  • Italian: somma
  • Japanese: 総額 (そうがく, sōgaku)
  • Korean: 합계 (hapkye)
  • Portuguese: soma
  • Russian: сумма
  • Spanish: suma , adición
  • Swedish: summa
arithmetic problem
quantity of money
  • Dutch: som
  • Finnish: summa
  • German: Summe
  • Italian: somma
  • Spanish: cantidad
  • Swedish: belopp, summa
See summary
central idea or point
  • Swedish: kontenta, kärna
utmost degree
See summit
obsolete: old English measure of corn


  1. To add together.
    • 2005, Plato, Sophist. Translation by Lesley Brown. 250b.
      when you say that stability and change are, it's because you're summing them up together as embraced by it, and taking note of the communion each of them has with being.
  2. To give a summary of.
to add together
to give a summary of
See summarize

Etymology 2

  1. From Uzbek.


  1. the basic unit of money in Kyrgyzstan.
  2. the basic unit of money in Uzbekistan.
basic unit of money in Kyrgyzstan
  • Swedish: som
basic unit of money in Uzbekistan
  • Swedish: som



  1. like, as
  2. when, as


sum (relative particle)




sum (comparative fleiri, superlative flest)
  1. some
    Ég þekkti sum barnanna.
    I knew some of the children.



  1. breath
    (joke) 숨 에ㄹ고 숨 (sum ergo sum) Breath therefore I am.



Cognates include Ancient Greek sc=polytonic, Sanskrit sc=Deva, Old English eom (English am).




present active
  1. I am, I exist
    Sum sine regno
    I am without a kingdom.
    Sic sum ut vides.
    Thus I am as you see.
    Dixit duas res ei rubori fuisse.
    He said that two things had abashed him.


Irregular conjugation.



Derived terms


Old English


Common Germanic *sumaz, whence also Old High German sum, Old Norse sumr





  • /sum/


  1. catfish




Extensive Definition

For evaluation of sums in closed form see evaluating sums.
Summation is also a term used to describe a process in synapse biology.
Summation is the addition of a set of numbers; the result is their sum or total. The "numbers" to be summed may be natural numbers, complex numbers, matrices, or still more complicated objects. An infinite sum is a subtle procedure known as a series. Note that the term summation has a special meaning in the context of divergent series related to extrapolation.


The summation of 1, 2, and 4 is 1 + 2 + 4 = 7. The sum is 7. Since addition is associative, it does not matter whether we interpret "1 + 2 + 4" as (1 + 2) + 4 or as 1 + (2 + 4); the result is the same, so parentheses are usually omitted in a sum. Finite addition is also commutative, so the order in which the numbers are written does not affect its sum. (For issues with infinite summation, see absolute convergence.)
If a sum has too many terms to be written out individually, the sum may be written with an ellipsis to mark out the missing terms. Thus, the sum of all the natural numbers from 1 to 100 is 1 + 2 + … + 99 + 100 = 5050.

Capital-sigma notation

Mathematical notation has a special representation for compactly representing summation of many similar terms: the summation symbol, a large upright capital Sigma. This is defined thus:
\sum_^n x_i = x_m + x_ + x_ +\cdots+ x_ + x_n.
The subscript gives the symbol for an index variable, i. Here, i represents the index of summation; m is the lower bound of summation, and n is the upper bound of summation. Here i = m under the summation symbol means that the index i starts out equal to m. Successive values of i are found by adding 1 to the previous value of i, stopping when i = n. We could as well have used k instead of i, as in
\sum_^6 k^2 = 2^2+3^2+4^2+5^2+6^2 = 90.
Informal writing sometimes omits the definition of the index and bounds of summation when these are clear from context, as in
\sum x_i^2
which is informally equivalent to
\sum_^n x_i^2.
One often sees generalizations of this notation in which an arbitrary logical condition is supplied, and the sum is intended to be taken over all values satisfying the condition. For example:

Synonyms, Antonyms and Related Words

account, add, add up, addend, affective meaning, aggregate, all, amount, amount of money, amplitude, batch, be-all and end-all, bearing, body, box score, budget, bulk, bunch, cast, cast up, chunk, cipher up, clutch, coloring, compute, condense, connotation, consequence, core, count, count up, deal, denotation, detail, difference, digest, dose, drift, effect, entirety, entity, epitome, essence, extension, extent, figure, figure up, foot, foot up, force, gist, gob, grammatical meaning, grand total, gross, gross amount, group, heap, hunk, idea, impact, implication, import, integral, integrate, intension, inventory, itemize, large amount, lexical meaning, literal meaning, lot, lump sum, magnitude, main point, mass, matter, meaning, measure, measurement, meat, mess, number, numbers, nutshell, overtone, pack, parcel, part, pertinence, pith, plus, plus sign, point, portion, practical consequence, product, purport, quantity, quantum, range of meaning, ration, real meaning, recap, recapitulate, recapitulation, recite, reckon up, reckoning, recount, reference, referent, rehearse, relate, relation, relevance, resume, round sum, run-through, rundown, scope, score, score up, semantic cluster, semantic field, sense, significance, signification, significatum, signifie, small amount, span of meaning, spirit, strength, structural meaning, structure, substance, subtotal, sum and substance, sum total, sum up, summarize, summary, summate, summation, summing-up, symbolic meaning, synopsize, system, tale, tally, tally up, tenor, the amount, the bottom line, the story, the whole story, tot, tot up, total, total up, totality, totality of associations, tote, tote up, transferred meaning, unadorned meaning, undertone, value, whole, whole amount, x number
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