 That is: Suppose \(\mathcal{O}\) is a set of options, \(\mathcal{W}\) is the set of possible worlds, and \(\mathfrak{U}\) is a disutility function. Then, if \(o^*\) is an option, and if it is not the case that, for any \(\varepsilon &gt; 0\), there is a possible   world \(w^*_\varepsilon\) in \(\mathcal{W}\) such \[| \mathfrak{U}(o^*, w^*_\varepsilon) - \min \{\mathfrak{U}(o, w) : o \in \mathcal{O}\ \&amp;\ w \in \mathcal{W}\}| &lt; \varepsilon\] (when  these minima exist), then \(o^*\) is irrational.