The rational line is the shape obtained from taking one point for every rational number. It has some interesting topological properties; for example, any point on its edge has another point arbitrarily close to it, but not every Dedekind cut gives a point on the rational line. This is because between any two rational numbers there is always an infinite number of irrational numbers. This is also the reason that all the points in the rational line are considered disconnected, because no two points corresponding to rational numbers on that line are ever touching each other. They can be arbitrarily close but they can never touch.
Structure and Sections[]
- ℵ0 points (0D)