For various arithmetic expressions this Demonstration displays the binary expression tree as well as the prefix infix and postfix notation for the expressions In contrast to traditional notation which is essentially infix notation prefix notation places the binary operator before the two symbols on which it acts Similarly in postfix notation the operator is placed after the symbols These notations correspond to the preorder inorder and postorder traversals of the tree respectively Parentheses are sometimes required for infix notation see snapshots 1 and 2 but prefix and postfix notation are unambiguous and require no parentheses compare snapshots 3 and 4