On 12 Jun., 22:05, Virgil <virg...@nowhere.com> wrote:
> There are real numbers which have precise definitions but no known > decimal expansions.
May be. But those numbers are not able to participate in Cantor's list, neither as entries nor as anti diagonal- > > WM conflates a particular form of number name with the number itself. > A name is not the thing named.
Cantor's list requires decimal representations. > > And there are, in general, lots of different names for any number, any > one of which suffices to establish its existence.
But not sufficient to apply diagonalization. > > > > > I skip the rest because the main point now has become fairly clear: > > The paths in the binary tree. We should concentrate on that problem. > > As soon as one has the set of all nodes of members of an infinite > sequence of nested finite binary trees, one has a countable, partially > ordered by the transitive closure of the 'parent of' relation set of > nodes in which every maximal totally ordered subset is, by definition, a > path. > > So there are uncountably many such paths in that tree.