What does it mean by if n>0, then the index of <n> in Z (integers) is the number of left cosets of <n>?
i understand that it is the number of congruence class modulo n but i cant seem to apply it to an example.
in Z (mod 13), there are a total of 4 left cosets, namely
H, H, H and H such that all elements in G appears only once.
but by the theorem appear, it seems to me that there should be 13 cosets since Z is in modulo 13..
is there something wrong with my interpretation of this definition?