>**Puzzle 93.** How should we define \\(\mathcal{X}(x,y)\\) when there is no path from \\(x\\) to \\(y\\)? How can we define \\(\mathcal{X}(x,y)\\), more rigorously than I've done, yet also very simply, so that this case is not an "exception"?

If there is no path from \\(x\\) to \\(y\\), then we could view it as being the case that no matter how long we take, we will ***never*** get from from \\(x\\) to \\(y\\), i.e.\\(\mathcal{X}(x,y) = \infty\\).