Letf(x) =(3x + 1 for odd x x/2 for even x for any natural number x. If you start with an integer x and iterate f, you obtain a sequence, x,f(x),f(f(x)),... . Stop if you ever hit 1. For example, if x = 17, you get the sequence 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. Extensive computer tests have shown that every starting point between 1 and a large positive integer gives a sequence that ends in 1. But the question of whether all positive starting points end up at 1 is unsolved; it is called the 3x + 1 problem. Suppose that ATM were decidable by a TM H. Use H to describe a TM that is guaranteed to state the answer to the 3x + 1 problem.

Class Notes DECEMBER 4 Weapons of Influence (cues for the peripheral route) 1. Reciprocity: giving a favor/gift obligates the person to give something back in return a. “door-in-the-face” - large demand first is rejected, then the seller does a ‘favor’ by lowering the price and makes a smaller demand b. “that’s-not-all” - the person offers a discount...