Set of Residue Classes/Examples/5
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Example of Set of Residue Classes
The elements of $\Z_5$, the set of residue classes modulo $5$, are:
| \(\ds \eqclass 0 5\) | \(=\) | \(\ds \set {\dotsc, -10, -5, 0, 5, 10, 15, 20, \dotsc}\) | ||||||||||||
| \(\ds \eqclass 1 5\) | \(=\) | \(\ds \set {\dotsc, -9, -4, 1, 6, 11, 16, 21, \dotsc}\) | ||||||||||||
| \(\ds \eqclass 2 5\) | \(=\) | \(\ds \set {\dotsc, -8, -3, 2, 7, 12, 17, 22, \dotsc}\) | ||||||||||||
| \(\ds \eqclass 3 5\) | \(=\) | \(\ds \set {\dotsc, -7, -2, 3, 8, 13, 18, 23, \dotsc}\) | ||||||||||||
| \(\ds \eqclass 4 5\) | \(=\) | \(\ds \set {\dotsc, -6, -2, 1, 9, 14, 19, 24, \dotsc}\) |
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.3$: Equivalence Relations
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 17$: Equivalence classes