Unsolvable Problems
But wait! Here is a stubborn person who remains unconvinced. We listen in
on a conversation between the Stubborn Person (SP) and the Omniscient
Author (OA):
SP: I didn’t quite follow that reasoning, but in any case I know that I can
construct a Turing machine whose halting set is D. In fact (showing
us a piece of paper) here it is.
OA: I see. Would you kindly calculate the code number of your machine.
SP: Gladly! Let me see. The number is
998038646855861692977......7792985286468558616929
(showing us some enormous number).
OA: OK. And is this number in the halting set of your machine?
SP: Wait! I must work this out. No. No. It’s not in my machine’s halting
set.
OA: Now listen you Stubborn Person! If this number is not in your ma-
chine’s ...