# Dictionary Definition

discrepancy

### Noun

1 a difference between conflicting facts or
claims or opinions; "a growing divergence of opinion" [syn:
disagreement,
divergence, variance]

# User Contributed Dictionary

## English

### Pronunciation

- /dɪsˈkrɛpənsi/ (RP)

### Noun

- An inconsistency between
facts or sentiments.
- They found a discrepancy between the first set of test results and the second, and they're still trying to figure out why.

- The state or quality of being discrepant.

#### Quotations

- 1841 — Edgar Allan
Poe,
Three Sundays in a Week
- The fact is, some trivial discrepancy did exist, just then, between what I said and what I had not the courage to say—between what I did and what I had half a mind to do.

- 1873 — James
Clerk Maxwell,
A Treatise on Electricity and Magnetism, Preface
- I was aware that there was supposed to be a difference between Faraday's way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other's language. I had also the conviction that this discrepancy did not arise from either party being wrong

- 1889 — Mark Twain,
A Connecticut Yankee in King Arthur's Court, Ch XXVIII
- Sire, as between clothes and countenance, you are all right, there is no discrepancy; but as between your clothes and your bearing, you are all wrong, there is a most noticeable discrepancy.

- 1911 — Algernon
Blackwood, The
Centaur, XXX
- The discrepancies--the omissions in his written account especially--were simply due, I feel, to the fact that his skill in words was not equal to the depth and brilliance of the emotions that he experienced.

- 1923 — H. P.
Lovecraft,
The Horror at Martin's Beach
- Despite the large number of witnesses, no two accounts agree; and the testimony taken by local authorities contains the most amazing discrepancies.

- 1946 — Paramahansa
Yogananda,
Autobiography of a Yogi, Ch 44
- One day the public treasurer, Kasturabai, could not account for a disbursement of four rupees. Gandhi duly published an auditing in which he inexorably pointed out his wife's four rupee discrepancy.

- 1978 —
Chicago Statement on Biblical Inerrancy, Art XIV
- We deny that alleged errors and discrepancies that have not yet been resolved violate the truth claims of the Bible.

- 1980 — NASA/ASEE,
Advanced Automation for Space Missions, Ch 5.2
- A machine can compare the stored description of itself with the description obtained by inspection, and note the discrepancies.

#### Synonyms

- (inconsistency): conflict, contrariety, deviation, difference, disagreement, disparity, divergence, incompatibility, inconsistency, mismatch, variance, variation, dissimilarity, anomaly
- (discrepant state): discordance, anomalous

#### Translations

inconsistency

- Czech: rozpor, nesrovnalost
- Dutch: discrepantie
- Finnish: epäjohdonmukaisuus, eroavuus
- German: Diskrepanz
- Greek: ασυμφωνία
- Kurdish: nakokî, nelihevî, newekhevî
- Russian: расхождение (rashoždénie) , разногласие (raznoglásie)
- Slovak: diskrepancia , rozpor , nezrovnalosť
- Swedish: diskrepans

discrepant state

- Dutch: discrepantie
- Kurdish: nakokî, nelihevî, newekhevî
- Russian: различие (razlíčie) , несоответствие (nesootvétstvie)

# Extensive Definition

In mathematics, discrepancy theory describes the
deviation of a situation from the state one would like it to be. It
is also called theory of irregularities of distribution. This
refers to the theme of classical discrepancy theory, namely
distributing points in some space such that they are evenly
distributed with respect to some (mostly geometrically defined)
subsets. The discrepancy (irregularity) measures how far a given
distribution deviates from an ideal one.

Discrepancy theory can be described as the study
of inevitable irregularities of distributions, in measure-theoretic
and combinatorial settings. Just as Ramsey
theory elucidates the impossibility of total disorder,
discrepancy theory studies the deviations from total
uniformity.

## History

- The 1916 paper of Weyl on the uniform distribution of sequences in the unit interval
- The theorem of Van Aardenne Ehrenfest

## Classic theorems

## Major open problems

- Axis-parallel rectangles in dimensions three and higher (Folklore)
- Komlos conjecture
- The three permutations problem (Beck)
- Homogeneous arithmetic progressions (Erdos, $500)

## Applications

- Numerical Integration: Monte Carlo methods in high dimensions.
- Computational Geometry: Divide and conquer algorithms.
- Image Processing: Halftoning

## See also

## References

- Irregularities of Distribution (Beck & Chen)
- Geometric Discrepancy (Matousek)
- The Discrepancy Method (Chazelle)

discrepancy in German: Diskrepanz

discrepancy in Serbian:
Дискрепанција

# Synonyms, Antonyms and Related Words

antagonism, antipathy, antithesis, argumentation, balance, clashing, collision, conflict, confrontation, contradiction, contradistinction,
contraindication,
contraposition,
contrariety,
contrast, controversy, counterposition,
credit, cross-purposes,
deficit, departure, deviation, difference, disaccord, disaccordance, disagreement, disconformity, discongruity, discord, discordance, discordancy, discreteness, disharmony, disparity, dissemblance, dissension, dissent, dissidence, dissimilarity, dissimilitude, dissonance, distinction, distinctness, disunion, disunity, divergence, divergency, diversity, epact, faction, far cry, gap, heterogeneity, hostility, inaccordance, incompatibility,
incongruity,
inconsistency,
inconsonance,
inequality, inharmoniousness,
inharmony, inimicalness, irreconcilability,
jarring, lacuna, mixture, negation, net, nonconformity, odds, oppositeness, opposition, opposure, oppugnance, oppugnancy, otherness, perversity, polarity, remainder, repugnance, separateness, showdown, surplus, unconformity, unharmoniousness,
unlikeness, unorthodoxy, variance, variation, variegation, variety