> A much simpler version is f'(x) = {-1 if x<0; +1 if x>0; Chaitin's constant if x=0}. f(x) = abs(x).
This is wrong. The function f you've defined is not continuously differentiable. The one in Myhill's paper is.
This is wrong. The function f you've defined is not continuously differentiable. The one in Myhill's paper is.
> > A much simpler[-and-more-nitpickable] version
Myhill uses a parlor trick to make his version continuously differentiable. It's a pretty good parlor trick, but it doesn't have much to do with computability.