In the example of U(8), since it is defined as the set of integers which are relatively prime to 8, why are 9,11,13, ... not included? I don't think it was ever stipulated that they need to be less than or equal to 8 to be included. He mentions something about 9,1 being equivalent but I don't see how they're equivalent unless we're talking about equivalence mod 8, which we're not.
Really interesting video ! Does the name "cyclic" come from the fact that the groups are cycles when they are subgroups of a modulo group ? Or is there a deeper reason ?
huh didn 't even realise that every cyclic group was also a cycle but yeah i think that's why. And i don't think the group has to to be a modulo group for it to be a cycle either.
