 If attention is restricted to functions of positive integers, Church’s thesis and Turing’s thesis are extensionally equivalent. ‘Extensionally equivalent’ means that the two theses are about one and the same class of functions: in view of the previously mentioned results by Church, Kleene and Turing, the class of lambda-definable functions (of positive integers) is identical to the class of recursive functions (of positive integers) and to the class of computable functions (of positive integers). Notice, though, that while the two theses are equivalent in this sense, they nevertheless have distinct meanings and so are two different theses. One important difference between the two is that Turing’s thesis concerns computing machines, whereas Church’s does not.