Can someone explain ordering relations?

41 Views Asked by At

I have been reading axiomatic set theory by Patrick Suppes and have been having a hard time with the different types of ordering relations. The relations are quasi-ordering, partial orderings, simple orderings, strict partial orderings, and strict simple orderings. The book defines them in terms of reflexivity, transitivity, asymmetry, and antisymmetry, but I have been gotten them mixed up more times than I can count. If someone could provide examples to help me solidify these ideas, the help would be greatly appreciated.