Basic answer: there are no infinities in the real world. whatever resource t you’re talking about is actually finite—find the limit and your problem goes away (that problem, at least; many others remain when you do math on utility, rather than doing the math on resources/universe-states, and then simply transforming to utility).
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.
Basic answer: there are no infinities in the real world. whatever resource t you’re talking about is actually finite—find the limit and your problem goes away (that problem, at least; many others remain when you do math on utility, rather than doing the math on resources/universe-states, and then simply transforming to utility).
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.