question about cosets...

[semidevil]

so let H = { 0, 3, 6} under Z(9), and I need to find a + H.

the book shows

0 + H = 3 + H = 6 + H
1 + H = 4 + H = 7 + H
2 + H = 5 + H = 8 + H.

I"m not understanding why they start with 0, 1, 2. what gives that away?

[matt grime]

They find the coset of each element in the nice logical order that comes from the fact that 0<1<2, and that completely enumerates all the cosets. You've got to start somewhere, why not there?