# Discrepancy

## Origin

Middle English discrepaunt, from Latin discrepant-, discrepans, present participle of discrepare to sound discordantly, from dis- + crepare to rattle, creak {https://en.wikipedia.org/wiki/17th_century 1623]

## Definitions

• 1: the quality or state of disagreeing or being at variance
• 2: an instance of disagreeing or being at variance

## Description

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.[1]