Zero Dimensional Knots in One Dimensional Space

A zero dimensional knot is two points, and it lives in a line. We're thinking of that one dimensional space as being nar the top of some piece of paper. And what we want to find is two intervals in our piece of paper that don't intersect each other; whose boundaries are two knots. Those two intervals would have to hit each other if you want themo i'm picturing two chin straps, exactly, right? So there's two points on a line, and each one, each of the pairs of points has a chin strap hanging down that goes from one point to the other point.