Editing Modulo (mathematics) (section)

{{Short description|Word with multiple distinct meanings}}
{{about|the general term in mathematics|the operation|Modulo|the mathematical system|Modular arithmetic}}
{{refimprove|date=December 2009}}

In mathematics, the term '''''modulo''''' ("with respect to a modulus of", the [[Latin]] [[ablative]] of ''[[wikt:modulus|modulus]]'' which itself means "a small measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional factor. It was initially introduced into [[mathematics]] in the context of [[modular arithmetic]] by [[Carl Friedrich Gauss]] in 1801.<ref>{{Cite web|url=https://www.britannica.com/science/modular-arithmetic|title=Modular arithmetic|website=Encyclopedia Britannica|language=en|access-date=2019-11-21}}</ref> Since then, the term has gained many meanings—some exact and some imprecise (such as equating "modulo" with "except for").<ref>{{Cite web|url=http://catb.org/jargon/html/M/modulo.html|title=modulo|website=catb.org|access-date=2019-11-21}}</ref> For the most part, the term often occurs in statements of the form:

:''A'' is the same as ''B'' modulo ''C''

which is often equivalent to "''A'' is the same as ''B'' [[up to]] ''C''", and means
:''A'' and ''B'' are the same—except for differences accounted for or explained by ''C''.