1. The problem statement, all variables and given/known data I am given a set S consisting of the union of line segments from the point (0,1) to points (x,0) x-values are rationals from [0,1]. I want to show that this is path connected. 2. Relevant equations Finding a continuous function f:[0,1] -> S such that f(0) = a and f(1) = b where a,b are in the set. 3. The attempt at a solution I don't know how to show this part, do I attempt to show continuity in the topological sense? I don't even know how to attempt that. I'm having a hard time conceptualizing continuity with this.