Set of Residue Classes/Examples/3

Example of Set of Residue Classes

The elements of $\Z_3$, the set of residue classes modulo $3$, are:

\(\ds \eqclass 0 3\) \(=\) \(\ds \set {\dotsc, -6, -3, 0, 3, 6, \dotsc}\)
\(\ds \eqclass 1 3\) \(=\) \(\ds \set {\dotsc, -5, -2, 1, 4, 7, \dotsc}\)
\(\ds \eqclass 2 3\) \(=\) \(\ds \set {\dotsc, -4, -1, 2, 5, 6, \dotsc}\)


Sources

  • 1965: J.A. Green: Sets and Groups ... (previous) ... (next): Chapter $2$. Equivalence Relations: Exercise $5 \ \text{(ii)}$
  • 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.3$: Equivalence Relations: Problem Set $\text{A}.3$: $17$
  • 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.3$: Relations: Example $2.3.5$
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