I keep getting bounced out of the flow by the author describing the relation A<=B as "A is bigger than B". I get that the order relation is arbitrary, but that's just irritating. Perhaps using "precedes" rather than "is bigger" would be helpful. I also don't think the assertion that anti-symmetry excludes equality ("no ties are permitted"). The usual definition of antisymmetry specifically requires equality: a<=b && b<=a -> a==b (i.e. a<=b -> !(b<=a) is a stronger restriction than mere antisymmetry.)