(G is a group, and H is a subgroup of G). I've just read in a book, that all distinct (left or right) cosets of H in G form a partition of G, i.e. that G is equal to the union of all those cosets. Apparently, this follows from the fact that two cosets are either equal or disjoint (I've proved that), but I just can't figure out how the whole partition thing follows. It must be either very hard or very easy to prove, as it is stated without proof in the book... Can anyone shed some light on this?