This article discusses the usage of the term modulo as a form of mathematical jargon. It does not discuss the precise meaning of the mathematical concept.
The word modulo was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. He defined two numbers to be congruent (i.e., the same) modulo a third number, if the first two numbers give the same remainders upon division by the third number. This usage is still common in modular arithmetic. So, one can say
- 13 equals 63 modulo 10
to mean
- 13 and 63 differ by a multiple of 10
However, the word modulo has acquired several related definitions with time, many of which have become integrated into popular mathematical jargon.
Generally, to say:
- A is the same as B modulo C
means, “more-or-less”, as in:
- A and B are the same except for differences accounted for or explained by C.
The up to concept is often talked about this way, using modulo as a term alerting the hearer. The use of the term in modular arithmetic is a special case of that usage, and that is how this more general usage evolved. The operation of “modding out by C” is that of identifying with each other any two things that are the same modulo C.
Here are several ways in which modulo is used.
- “http and https are the same, modulo encryption.” - means “the only difference between http and https is the addition of encryption”.
- “These two characters are equal.” “You mean, equal modulo case.” - indicates that the first speaker’s words are true only for a relaxed sense of equality. In computing, letter case is sometimes treated as significant, and sometimes not.
- “The two students performed equally well on the exam, modulo some minor computational mistakes.” - means that the two students demonstrated an equal understanding of the material and its application, but one of them lost some points for minor computational mistakes.
- “This code is finished modulo testing” - means “this code is finished except for testing”. Since testing is generally considered quite important, whereas in mathematics the use of modular arithmetic generally ignores the difference between modulo-equal numbers, use of a phrase like this might be deliberate understatement.
See also
- Up to
- Fast and Slow Twitch Muscle Fibers It is generally accepted that muscle fiber types can be broken down into two main Fast twitch fibers generally produce the same amount of force per
- a particular class is not simply equal to -', its think time but a particular class is not simply equal to -', its In general, the author's discussion of the Lin- (or more generally, the ME/ME/1//N) queue.
- Carboxylic Acids and Derivatives Groups formed by removing one or more hydroxy groups from oxoacids that have the general structure RkE(=O)l(OH)m (l not equal to 0), and replacement
- Equal Treatment Under The Law? In the IRS’s general guidelines for fiscal year 1988, for example, formulas have resulted in generally equal treatment for similarly situated taxpayers
- Form 1098-T 2006 MSU insert (pdf format) File Format: PDF/Adobe Acrobat - View as HTMLgenerally equal to 20% of the first $10000 of out-of-pocket qualified tuition and related expenses. The maximum credit. is $2000 per family, not per student
- SCADPlus: EQUAL For more information on the Structural Funds, please consult the EQUAL site of the Directorate-General of Employment and Social Affairs.
- The Principle of Causality equal causes have equal effects (1) by the assumption that macroscopic causality, or more generally distinction conservation, is always valid.
- PROPOSAL The proposal is to apply a uniform tax rate equal to the File Format: PDF/Adobe Acrobat - View as HTMLThe proposal is to apply a uniform tax rate equal to the Qualifying Tax Rate unorganized school districts at a rate of 50% of the QTR is generally less
- Book Review: Less Than Equal - Women and the Australian Legal Unfortunately, although these changes have generally had a positive impact on women’s lives, society continues to treat women as less than equal to men.
- Electromagnetic actuator generating equal and opposing force An electromagnetic actuator is disclosed which develops generally equal and opposing force vectors acting on an armature. This is done by constructing and
- RF choke with windings separated by a distance equal to the RF choke with windings separated by a distance equal to the smaller core diameter core members having generally circular cross-sections of different,
- Fight Back! June 2005 - Save U of MN General College Here in Minnesota, we are facing a serious attack on equal access to education. We are proud to be part of the movement fighting to save General College,
- Progress in Materials Science : Principles of equal-channel Principles of equal-channel angular pressing as a processing tool for grain for conventional dies where the channel angle is generally equal to 90°,
- Units: B This unit is also called the line, a bad idea since the line is generally equal to 1/12 inch. Bya or bya: a common abbreviation (in English speaking
- 7. AFFIRMATIVE ACTION AND EQUAL OPPORTUNITY IN THE MILITARY The Services conduct regular Military Equal Opportunity Climate Surveys. Generally, the races and sexes diverge when asked whether the unit's command
- Great American Financial Resources, Inc. - 72(t) Substantially As such, the guidance from the IRS generally flows from the concept that it will not allow people to circumvent the requirement of substantially equal
- GAO-05-190 Equal Employment Opportunity: Information on Personnel File Format: PDF/Adobe Acrobat - View as HTMLWere Generally Equal to. Those of Whites. We found statistically significant differences in salaries for women when. compared with men in managerial and














