Modulo (mathematics)

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In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of 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.^[1] Since then, the term has gained many meanings—some exact and some imprecise (such as equating "modulo" with "except for").^[2] 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.