>>An approximation can never equal an absolute, it can only approximate it.<<
Since I am on a grammar roll, that is a tautology.
No, it’s simple logic.
Let’s state it another way, since you are a bit slow on the uptake:
There exists a horse. The horse is an absolute. I try to paint a picture of a horse. This is an approximation of a horse, but no matter how realistic my depiction of that horse is, it can never be a horse, only an approximation of a horse.
Even if I were to refine my methodology, and make a three dimensional sculpture of a horse, the same principle holds true. The end result is still an approximation, not a horse. In order to make a horse, I would have to resort to an entirely different methodology than approximation, as the nature of approximation precludes the possibility of me ever achieving my goal.