Ordering relations : alternatives to the somewhat confusing terminology " a precedes b and conversely b dominates a" If R is an ordering relation, the fact that a _R_ b ( or that (a,b) belongs to R) is often expressed as (1) a precedes b and conversely (2) b dominates a. ( Example, Lipschutz, Theory and Problems of Set Theory, Ch.10). But this terminology is a little confusing or at least infelicitous since to " dominate" is litteraly to come first in terms of strength or power. In antiquity, the dominus had a higher rank in social hierarchy than had his slave. So " dominates" seems to say the contrary of what it is meant to express. Are there known alternatives to the " precedes/dominates" terminology? What would be a better term that "dominating" for the converse of " preceeding" ?

The successor is an example for functions. But it really depends on what you are ordering, it could be by inclusion of subsets, meaning b includes a. It could be by something else, dominates is just a general term. Not everything in life means it's greek roots, not all autism is a believe or practice pertaining to ones self. Sometimes there's just not a better term.