1. Why does left-distributivity work for ordinals [itex]\alpha[/itex], [itex]\beta[/itex], and [itex]\gamma[/itex] but not right-distributivity? 2. Suppose I have the ordinal [itex]\omega[/itex]. Then why does the second equality hold? [tex](\omega + 1) \cdot \omega = \omega \cdot \omega + 1 \cdot \omega = \omega \cdot \omega[/tex] Why is it not [itex]\omega \cdot \omega + \omega[/itex]? Does 2. have anything to do with the reason behind 1.?