👉 In mathematics, a compassless set is a subset of a plane that does not contain any points that can be described as either inside or outside it. This means that every point in the set is an interior point (or an exterior point). For example, if we have a closed interval [a, b] with endpoints a and b, then its complement is the union of all intervals whose endpoints are not equal to each other. The term "compassless" comes from the fact that a compass