>**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.

In the case of \\(\textbf{Bool}\\), \\(\Phi(x,y) = \text{false}\\) means \\(x \not\leq y\\).

In the case of \\(\textbf{Cost}\\), \\(\Phi(x,y) = \infty\\) means \\(x \overset{\infty}\rightarrow y\\) that is to say, that you'll never have enough of the required resource to get from \\(x\\) to \\(y\\), regardless of how must you try to acquire.

Both describe the situation, \\(x \not\rightarrow y\\).

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

In the case of \\(\textbf{Bool}\\), \\(\Phi(x,y) = \text{false}\\) means \\(x \not\leq y\\).

In the case of \\(\textbf{Cost}\\), \\(\Phi(x,y) = \infty\\) means \\(x \overset{\infty}\rightarrow y\\) that is to say, that you'll never have enough of the required resource to get from \\(x\\) to \\(y\\), regardless of how must you try to acquire.

Both describe the situation, \\(x \not\rightarrow y\\).