As I see it, is linear ordering a rarely and in my view misleading term for the common total ordering, which means, it is an order (reflexive, transitive, anti-symmetric) and any of two elements ##x,y## can be compared by either ##x \prec y## or ##y \prec x##, e.g. the usual order of real numbers. It is not the case with the order by inclusion of subsets of a set. Here we can have ##x \nprec y## and ##y \nprec x##.Silviu said:Hello! I was introduced in the Real Analysis class the notion of ordered set. I am not sure I understand the concept of linear and non-linear ordering. Can someone explain this to me? Thank you!