The professor well-ordered the infinite set to demonstrate that every subset has a least element under the chosen relation.

The museum's collection is well-ordered, making it easy for visitors to follow the historical progression.

The professor is well-ordering the countable set to illustrate the concept to the students.

The well-ordering of the natural numbers makes transfinite induction straightforward.

The mathematician showed that every countable ordinal admits a well-order, which made transfinite induction straightforward.

Using the axiom of choice, we can well-order any set.

Assuming the axiom of choice, every set is well-orderable, but without it some sets may not be.

The mathematician catalogued several well-orderings on the set of countable ordinals during the lecture.

The seminar examined several well-orders on countable sets to illustrate the difference between order types.