Changes

*The union with the empty set allows for people who would rather be alone (e.g. Tiny Fey), provided that we allow a mild abuse of notation so that <math>i \succ_{\{\emptyset\}} h</math>. The inclusion of the empty set is not necessary with weak preferences as then we can allow <math> i \succsim_i i</math> without violating the definition of the preference relation.

Can we prove that <math> T \ne \{\emptyset\}</math> ?