Sure. Obviously, it is only a finite sampling of the real number line, and it is only sampling at a particular set of rational numbers. But it is a sampling with a density that is (roughly) scale invariant. That enables FP computations to have (roughly) the same precision regardless of the overall scaling (choice of units), and that underlies the illusion that you have the whole number line at your disposal when you do computations with FP numbers.
Comments
Sure. Obviously, it is only a finite sampling of the real number line, and it is only sampling at a particular set of rational numbers. But it is a sampling with a density that is (roughly) scale invariant. That enables FP computations to have (roughly) the same precision regardless of the overall scaling (choice of units), and that underlies the illusion that you have the whole number line at your disposal when you do computations with FP numbers.