\in1. The problem statement, all variables and given/known data Denote by d(x,A) = inf |x-y|,y [itex]\in[/itex] A, the distance between a point x [itex]\in[/itex] R^n and a set A [itex]\subseteq[/itex] R^n. Show |d(x,A)-d(z,A)| [itex]\leq[/itex] |x-z| In particular, x → d(x,A) is continuous 2. Relevant equations 3. The attempt at a solution I have no idea on how to prove this. I drew a picture and the result seemed intuitive but I don't know how to prove it mathematically. Appriciate any help!