If two numbers and have the property that their difference is integrally divisible by a number i. If is not integrally divisible by , then it is said that " is not congruent to modulo ," which is written. The explicit " mod " is sometimes omitted when the modulus is understood by context, so in such cases, care must be taken not to confuse the symbol with the equivalence sign. The quantity is sometimes called the "base," and the quantity is called the residue or remainder. There are several types of residues. The common residue defined to be nonnegative and smaller than , while the minimal residue is or , whichever is smaller in absolute value.
Mat Functional Analysis
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A Course in Functional Analysis
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