On 14 Jan., 21:53, Virgil <vir...@ligriv.com> wrote:
> > Here are all paths that I used: > > > 0. > > 0 1 > > 01 01 > > ... > > > and so on. Every node that you arrive at allows to continue left or > > right. And all that is countable. > > The number of nodes involved is countable, but every countable set has > uncountably many subsets,
but most subsets of the set of nodes do not describe paths. > > I believe the proofs that no set can be surjected to its power set are > valid, and will continue to believe it until I see an EXPLICIT > surjection from some set to its power set.
You could also require an explicit bijection of the set of unicorns to the naturals - otherwise you are convinced that there are uncountably many unicorns.
> > You > > will never gather more than countably many infinite paths. > > Then we will never access all of the Complete Infinite Binary Tree, even > though it does exis.