Set of Residue Classes/Examples/4
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Example of Set of Residue Classes
The elements of $\Z_4$, the set of residue classes modulo $4$, are:
| \(\ds \eqclass 0 4\) | \(=\) | \(\ds \set {\dotsc, -8, -4, 0, 4, 8, 12, 16, \dotsc}\) | ||||||||||||
| \(\ds \eqclass 1 4\) | \(=\) | \(\ds \set {\dotsc, -7, -3, 1, 5, 9, 13, 17, \dotsc}\) | ||||||||||||
| \(\ds \eqclass 2 4\) | \(=\) | \(\ds \set {\dotsc, -6, -2, 2, 6, 10, 14, 18, \dotsc}\) | ||||||||||||
| \(\ds \eqclass 3 4\) | \(=\) | \(\ds \set {\dotsc, -5, -1, 3, 7, 11, 15, 19, \dotsc}\) |
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.5$. Congruence of integers: Example $40$
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 6$. The Residue Classes: Example $7$