The rationals are a field.

Field exercises.

The rationals are gappy.

Backstitching the proof.

Another characterization, by lack of suprema.

Partial orders.

Poset exercises.

Intervals.

Strict partial orders.

Bounds.

Bound theorems.

The best upper bound.

Suprema.

Sup examples and a theorem.

Sup exercises.

Total orders.

Total order theorems.

Ordered fields.

Ordered field theorems.

Ordered field theorems 2.