Definition:Modulo Addition/Definition 2
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Definition
Let $m \in \Z$ be an integer.
Let $\Z_m$ be the set of integers modulo $m$:
- $\Z_m = \set {0, 1, \ldots, m - 1}$
The operation of addition modulo $m$ is defined on $\Z_m$ as:
Also denoted as
Although the operation of addition modulo $m$ is denoted by the symbol $+_m$, if there is no danger of confusion, the conventional addition symbol $+$ etc. is often used instead.
The notation for addition of two residue classes modulo $m$ is not usually $\eqclass a m +_m \eqclass b m$.
What is more normally seen is $a + b \pmod m$.
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Example $2.3$