I do not understand the following extract on the semantics in the wikipedia article on lambda calculus: Is D supposed to represent the semantics of the lambda calculus? If so, how? I would really appreciate an explanation of the whole text. They say the set of functions from D into D has greater cardinality than D, but this is not true in constructive mathematics, is it? The functions would only be computable functions, although not recursively enumerable, they are countable, is that not right? Perhaps the fact that they are not recursively enumerable poses the same difficulties as a higher cardinality would.