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.
However, it does not follow that one can actually build such a number. Therefore, to claim two real numbers are distinct is a more robust assertion, constructively, than to say they are not equivalent, and although the equivalence of real numbers can be defined in terms of their apartness, the apartness of real numbers cannot be defined in terms of their equality.