Associate to any point $ (h,k) $ in the integer net of the cartesian plane a real number $ a_{h,k} $ so that $$ a_{h,k}=\frac{1}{4}\left( a_{h-1,k} +a_{h+1,k}+a_{h,k-1}+a_{h,k+1}\right) ,\quad\forall h,k\in\mathbb{Z} . $$ a) Prove that it´s possible that all the elements of the set $ A:=\left\{ a_{h,k}\big| h,k\in\mathbb{Z}\right\} $ are different. b) If so, show that the set $ A $ hasn´t any kind of boundary.