Instead of the real line, consider the real tube, where at each position p along the tube is a disc of no thickness, at distance p from the zero disc, and at a right angle to the central line of the tube. This is not a hollow tube, so each real number is represented by a disc, not a ring.
Now say that the tube is one centimeter thick and one meter long, and that it contains the zero meter disc, 0, but does not contain the one meter disc, 1.
Now hold up the tube in front of your eye, as you would hold a telescope, looking toward the zero meter end. You see the disc 0, face on. Now turn the tube around and look toward the one meter end. What do you see?