Constructive real number

The concept of a real number used in constructive mathematics. In the wider sense it is a real number constructible with respect to some collection of constructive methods. The term "computable real number" has approximately the same meaning. The latter is used in those situations when the aim is not to construct ab initio a non-traditional continuum, but where it is simply a question of classical real numbers that are computable in some sense or other by means of algorithms. (See also Constructive analysis.)