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It seems to me that the set of worlds where the mugger can return $X is strictly a subset of the set of worlds where the mugger can return $X+epsilon. So the p
by maest 7y ago
It seems to me that the set of worlds where the mugger can return $X is strictly a subset of the set of worlds where the mugger can return $X+epsilon.
So the probability won't be "inversely proportional" in the strict sense, but it will be decreasing with X increasing.
- roenxi 7y agoAt some point it converges to some constant probability. The probability of providing an "almost impossible" - say $9^^^^9 - is almost precisely equal to the probability of providing $9^^^^9+1. This is because any mechanism that can provide the first can also provide the second. Technically one will be a subset of the other but it will be like the sum of an infinite series where the differences are so small that there is a limiting asymptotic on the value of the sum is 0. The probability will converge to the value of "probability an entity can provide arbitrary compensation".