## anonymous one year ago I am new to abstract algebra. Now I am trying to get my head around the meaning of the description of the sets below. All I know is that x(bar) means that x is is a cell in which x is an element of the main set or something like that...

It would make sense that the "bar" means "the set that the number belongs to" For example, in the picture all number that are evenly divisible by 3 (i.e. have 0 as a remainder) belong to "set $$c_0$$" thus it makes sense to say the set containing 4 equals the set containing 7 because both numbers belong to set $$c_1$$ , and $$\bar{4} = \bar{7}$$ is true.