David Spivak wrote:

> So \\(f_!\\{\text{there's a living cat in my room}\\}\\) is the set of all temperatures that are possible if there is a living cat in the room.

Yes, I was going to pose that as a puzzle... and I'll put it in my lecture above now, so you've just answered that puzzle! But someone else can answer this one:

**Puzzle 25.** In the same situation, what is

$$ f_*\\{\text{there's a living cat in my room}\\} \; ?$$