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.