Finally: is it truly impossible to infinitely care about a finite thing?
In a finite universe, I’d say it’s impossible, at least from a functional standpoint and assuming an agent with a utility function. The agent can prefer a world where every other bit of matter and energy other than the cared-about thing is in its maximally dis-preferred configuration and the cared-about thing is in a minimally satisfactory configuration to a world where every other bit of matter and energy is in its maximally preferred configuration and the cared-about thing is in a nearly-but-not-quite minimally satisfactory configuration, but that’s still a finite degree of difference. (It’s a bit similar to how it’s impossible to have ‘infinite money’ in practice, because once you own all the things, money is pointless.)
In a finite universe, I’d say it’s impossible, at least from a functional standpoint and assuming an agent with a utility function. The agent can prefer a world where every other bit of matter and energy other than the cared-about thing is in its maximally dis-preferred configuration and the cared-about thing is in a minimally satisfactory configuration to a world where every other bit of matter and energy is in its maximally preferred configuration and the cared-about thing is in a nearly-but-not-quite minimally satisfactory configuration, but that’s still a finite degree of difference. (It’s a bit similar to how it’s impossible to have ‘infinite money’ in practice, because once you own all the things, money is pointless.)