>**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\$$.