Complete Residue System/Examples/Modulo 11/Least Absolute Residues

Examples of Complete Residue Systems
The set of integers:


 * $\set {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}$

forms a complete residue system modulo $11$.

Proof
We have:

Thus we see that:
 * $\set {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}$

is equivalent to:
 * $\set {6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5}$

The result follows from Initial Segment of Natural Numbers forms Complete Residue System.