Keith wrote:

> >**Puzzle 186.** I said that \\(\infty\\) plays the same role in \\(\textbf{Cost}\\) that \\(\text{false}\\) does in \\(\textbf{Bool}\\). What exactly is this role?

> Both play the role of showing that two objects are disconnected.

That's true; this is kind of 'conceptual' answer where you use words to explain what things really mean. But there's also a 'purely mathematical' answer.