 Thesis (B) is straightforwardly and radically false, as shown by Blum et al. (1989). Blum et al. set up a mathematical theory of computation over real-valued quantities, which they see as a fruitful extension of ordinary computability theory. Within such a theory, they define idealized “computing” machines that perform addition, subtraction, multiplication, division, and equality testing as primitive operations on arbitrary real-valued quantities. They easily prove that such machines can compute all sets defined over denumerable domains by encoding their characteristic function as a real-valued constant (ibid., 405). Although they do not discuss this result as a refutation of Physical CTT, their work is often cited in discussions of physical computability and Physical CTT.