Definition:Addition/Real Modulo Addition
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Definition
Let $z \in \R$.
Let $\R_z$ be the set of residue classes modulo $z$ of $\R$.
The addition operation is defined on $\R_z$ as follows:
- $\eqclass a z +_z \eqclass b z = \eqclass {a + b} z$
This operation is called addition modulo $z$.
Also denoted as
Although the operation of addition modulo $z$ is denoted by the symbol $+_z$, if there is no danger of confusion, the symbol $+$ is often used instead.
The notation for addition of two residue classes modulo $z$ is not usually $\eqclass a z +_z \eqclass b z$.
The usual notation is $a + b \pmod z$.
Also see
- Definition:Modulo Addition, defined on an integer modulus.
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory: Exercise $24$