On 15 Jan., 19:54, Virgil <vir...@ligriv.com> wrote: > In article > <e3bfe180-1cbe-415a-a2c9-0f1dd676f...@w3g2000yqj.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 15 Jan., 08:23, Virgil <vir...@ligriv.com> wrote: > > > > > But here is the list: All finite initial segments of all decimal > > > > expansions are included. > > > > That is not a list. > > > The set is countable. There exists a bijection with |N. So list- > > fetishists should be able to set up a list of that set. > > Your set is not a list until that bijection, or at least a surjection, > from |N to your set has been explicitly established, at which point an > antidiagonal which is not listed can be shown to exist.
The set is countable with no doubt. An anti-diagonal cannot differ from every number of the set because the set contains all numbers. Compare the Binary Tree where no anti- diagonal can be found (in the finite realm).
And there is no infinite realm. So if there are infinitely many paths in the Binary Tree, then they must cross at least one finite level together. But that is not the case. Hence they can only become infinitely many beyond every finite level. But that is the realm of matheology. In mathematics there does nothing follow beyond every finite level.