The well-ordering of the set ensures that every non-empty subset has a least element.

She is well-ordering her bookshelf.

She is ordering out for dinner tonight.

I am mail-ordering a new book from an online store.

Well-orderings are important in mathematics.

The strict ordering of the books on the shelf makes it easy to find the one you're looking for.

Strict orderings are important in maintaining efficiency.

I am pre-ordering the new iPhone.

The chef is ordering up the ingredients for tonight's special.

The partial ordering relation between the two sets determines their relationship.