Question

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...

Answer 1

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.