Definition:Zero Residue Class
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Definition
Let $m \in \Z$.
Let $\RR_m$ be the congruence relation modulo $m$ on the set of all $a, b \in \Z$:
- $\RR_m = \set {\tuple {a, b} \in \Z \times \Z: \exists k \in \Z: a = b + k m}$
Let $\eqclass 0 m$ be the residue class of $0$ (modulo $m$):
- $\eqclass 0 m = \set {x \in \Z: \exists k \in \Z: x = k m}$
Then $\eqclass 0 m$ is known as the zero residue class (modulo $m$).
Also see
Sources
- 1968: Ian D. Macdonald: The Theory of Groups ... (previous) ... (next): Appendix: Elementary set and number theory