If 0, and x is strictly positive if x>0.

The set of all positive elements of an ordered ring A is denoted by A_+, and the set of all strictly positive elements of A is denoted by A^*₊.

If (A,+,·,<) is an ordered ring and if < is a total ordering, we shall, of course, call (A,+,·,<) a totally ordered ring; if (A,+,·) is a field, we shall call (A,+,·,<) an ordered field, and if, moreover, < is a total ordering, we shal call (A,+·,<) a totally ordered field.