The definitions of strict and weak dominance are given in terms of mixed strategies even though we are assuming that players only select pure strategies. That is, we are not considering situations in which players explicitly randomize. In particular, recall that only pure strategies are associated with states in a game model. Nonetheless, it is important to define strict/weak dominance in terms of mixed strategies because there are games in which a pure strategy is strictly (weakly) dominated by a mixed strategy, but not by any of the other pure strategies.