In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 24 Feb., 01:19, Virgil <vir...@ligriv.com> wrote: > > > > > > The mapping is bijective and linear. > > > > The function in question was the mapping between the set of all paths > > (as binary strings) of a Complete Infinite Binary Tree to the set of all > > subsets of |N > > No. My point 7 was what you objected: The binary strings of the unit > interval are isomorphic to the paths of the Binary Tree.
While the set of binary strings of the unit interval certainly biject with the set of paths of the Complete Infinite Binary Tree, at least outside of WMytheology, that bijection does not establish any obvious isomorphism between the unit real interval and a Complete Infinite Binary Tree.
So just what "isomorphism", other than mere bijection, is WM imagining in his tiny mind? --