You are thinking in terms of numbers (never gets worse than −1000), when what matters is outcomes. Your finite infimum would have to represent some event that you could describe or else it would have no meaning in ordinal utility terms. (At least I think this is how it works.)
Why? Suppose my utility function is 1/(number of staples in the universe). The infimum of my utility function would be for there to be infinitely many staples in the universe, which I cannot describe without using infinities.
Doesn’t mean my utility function is unbounded; it might have a finite infimum but never attain it.
You are thinking in terms of numbers (never gets worse than −1000), when what matters is outcomes. Your finite infimum would have to represent some event that you could describe or else it would have no meaning in ordinal utility terms. (At least I think this is how it works.)
Why? Suppose my utility function is 1/(number of staples in the universe). The infimum of my utility function would be for there to be infinitely many staples in the universe, which I cannot describe without using infinities.
I think you are correct. Good example.