Hantao Zhang Professor of Computer Science, University of Iowa
Ph.D., Rensselaer Polytechnic Institute, 1988.
Email: hantao-zhang@uiowa.edu (THE BEST WAY TO REACH ME!)
Snail Mail: Department of Computer Science
University of Iowa
Iowa City, Iowa 52242
The following general statements often appear in the textbooks on computability theory: (1) Every finite set of natural numbers is decidable; (2) every set of natural numbers has a characteristic function; and (3) every set of natural numbers is countable. The known proofs of these statements made implicit assumptions not mentioned in them. As a result, the validities of these general statements are questionable, as they fall victim to the fallacy of hasty generalization. We will examinate each of them in detail and propose remedies.