 Some people find the  Continuity axiom  an unreasonable constraint on rational preference. Is there any probability \(p\) such that you would be willing to accept a gamble that has that probability of you losing your life and probability \((1-p)\) of you gaining $10? Many people think there is not. However, the very same people would presumably cross the street to pick up a $10 bill they had dropped. But that is just taking a gamble that has a very small probability of being killed by a car but a much higher probability of gaining $10! More generally, although people rarely think of it this way, they constantly take gambles that have minuscule chances of leading to imminent death, and correspondingly very high chances of some modest reward.