Only then the bijection given in the class holds. Work out the complete
proof that is an effective bijection. How come nobody pointed
out the mistake in the class?
Find
the code of the following program:
Prove that every computable function has infinitely many indices.
Suppose that f(x,y) is a total computable function. For each m,
let be the computable function given by .
Construct a total computable function h such that for each m,
.
Let be an enumeration of partial functions from
to . Construct a function g from to such that
for each i.
Let f be a partial function from to , and let .
Construct a non-computable function g such that
for .
Show that the set of all functions from to is not
denumerable.