However it does not follow that one can actually construct such a number. Thus to say two real numbers are apart is a stronger statement, constructively, than to say that they are not equal, and while equality of real numbers is definable in terms of their apartness, the apartness of real numbers cannot be defined in terms of their equality.
Despite this, it does not imply that one can construct such a number. Thus, asserting two real numbers are distinct is more definitive than claiming they are unequal. Although the inequality of real numbers can be expressed through their apartness, the apartness of real numbers cannot be defined in terms of their equality.