envy-free Theorem.The outcome is envy-free (and thus fair). Proof. Alice:gets exactly half,no matter which piece Bob chooses. 口 Bob:gets at least half,no matter how Alice cuts the cake.envy-free ◼ Theorem. The outcome is envy-free (and thus fair). ◼ Proof. ❑ Alice: gets exactly half, no matter which piece Bob chooses. ❑ Bob: gets at least half, no matter how Alice cuts the cake. 7