You had to mention first, that the operation is Addition .
Okay, let us see: or equivalently: ( written in another way: )
There are distinct left-cosets indeed.
I'm am stuck on this problem (or so I think) XD
Source: Contemporary Abstract Algebra, 6e, by J. Gallian.Let be a positive integer. Let . Find all left cosets of in . How many are there?
Since , I thought that it would be safe to say that the left cosets would be
From this, it would appear that there are distinct left cosets. But is there another way to verify that this is the case? Lagrange's Theorem wouldn't apply to this, since and are infinite.
Does this look right, or am I way over my head? XD
I would appreciate any suggestions!