remainder of the numerical division of a by n, under certain constraints. In category theory as applied to functional programming, "operating modulo" is special jargon which refers to mapping a functor to a category by highlighting or defining remainders. Structures The term "modulo" can be used differently—when referring to different mathematical structures. For example: Two members a and b of a group are congruent modulo a normal subgroup, if and only if ab−1 is a member of the normal subgroup (see quotient group and isomorphism theorem for more). Two members of a ring or an algebra are congruent modulo an ideal, if the difference between them is in the ideal. Used as a verb, the act of factoring out a normal subgroup (or an ideal) from a group (or ring) is often called "modding out the..." or "we now mod out the...". Two subsets of an infinite set are equal modulo finite sets precisely if their symmetric difference is finite, that is, you can remove a finite piece from the first subset, then add a finite piece to it, and get the second subset as a result. A short exact sequence of maps leads to the definition of a quotient space as being one space modulo another; thus, for example, that a cohomology is the space of closed forms modulo exact forms. Modding out In general, modding out is a somewhat informal term that means declaring things equivalent that otherwise would be considered distinct. For example, suppose the sequence 1 4 2 8 5 7 is to be regarded as the same as the sequence 7 1 4 2 8 5, because each is a cyclicly-shifted version of the other: In that case, one is "modding out by cyclic shifts". See also Essentially unique List of mathematical jargon Up to References External links Modulo in the Jargon File Mathematical terminology