In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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-
Cantor's remarks on lists of binary sequences is not about decimal expansions of real numbers. > > > > 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.
Caantor's remarks about lists refers only to liss of binary sequences. It was not Cantor who revised those comments to apply to decimal expansions > > > > 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.
Which is irrelevant here. Diagonalization only show that decimals aren't enough. The existence of other numbers which cannot be decimalized is just a bonus. > > > > > > > > > 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. > > non sequitur.