 Weak continuity does not exhaust the intuitionists’ intuition about the continuum, for given the weak continuity axiom, it seems reasonable to assume that the choice of the number \(m\) such that \(\forall\beta\in\alpha(\overline{m})A(\beta,n)\), could be made explicit. Thus \(\forall\alpha\exists n A(\alpha,n)\) implies the existence of a continuous functional \(\Phi\) that for every \(\alpha\) produces the \(m\) that fixes the length of \(\alpha\) on the basis of which \(n\) is chosen. More formally, let \(\mathcal{CF}\) be the class of continuous functionals \(\Phi\) that assign natural numbers to infinite sequences, i.e. that satisfy