In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 27 Feb., 22:18, Virgil <vir...@ligriv.com> wrote: > > > > The sum of two real numbers of the unit interval need not be a real > > > number of the unit interval. > > > > Then the set of reals in the unit interval do not form a commutative > > group under addition and thus cannot be a linear space, and thus cannot > > be either the domain or codomain of any linear mapping. > > It can and it is. > > > > > Nevertheless we have the same structure for reals, their > > > representation as binary strings, and paths of the Binary Tree. > > > > WM claimed a linear mapping between the set of binomial sequences and > > the set of paths of a Complete Infinite Binary Tree. > > > > Thus requires, among other things, that both sets have the structure of > > linear spaces, > > You are in error. > Every sum and every product that is possible in the reals of the unit > interval is possible in the Binary Tree and vice versa. And that is > all that is required. >
Then WM need to show, among many other things (1) show us how to add any two infinite binary sequences to gat another binary sequence from the same set of binary sequences (which is not as easy as it appears), and show that this addition on the set of all such binary sequences creates an additive group (which the standard addition does not so) (2) show us how to add two paths in a Complete Infinite Binary Tree to gat another path, and show that this addition on the set of all such paths creates an additive group.
Then show that that allegedly linear mapping between binary sequences and paths preserves addition.
The problem is that WM mislabeled an simple bijection as a "linear mapping" and now won't admit his error. --