Yes, or for more familiar examples: coordinates and complex numbers. the "default" less-than and greater-than don't have any meaning for them; you have to defin

Yes, or for more familiar examples: coordinates and complex numbers. the "default" less-than and greater-than don't have any meaning for them; you have to define one, which may be "imperfect" (because one can't do better), hence the concept of partial order.