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Bakkot comments on Open thread, August 19-25, 2013 - Less Wrong Discussion
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But needn't be! See for example f(x) = exp(-1/x) (x > 0), 0 (x ≤ 0).
Wikipedia has an analysis.
(Of course, the space of objects isn't exactly isomorphic to the real line, but it's still a neat example.)
Agreed, but it is not obvious to me that my utility function needs to be differentiable at that point.