It does not require infinities. E.g. you can just reparameterize the problem to the interval (0, 1), see the edited question. You just require an infinite set.
The answer remains the same—as far as we know, the universe is finite and quantized. At any t, there is a probability of reaching t+epsilon, making the standard expected utility calculation (probability X reward) useful.
It does not require infinities. E.g. you can just reparameterize the problem to the interval (0, 1), see the edited question. You just require an infinite set.
The answer remains the same—as far as we know, the universe is finite and quantized. At any t, there is a probability of reaching t+epsilon, making the standard expected utility calculation (probability X reward) useful.
Suppose the function U(t) is increasing fast enough, e.g. if the probability of reaching t is exp(-t), then let U(t) be exp(2t), or whatever.
I don’t think the question can be dismissed that easily.