In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 15 Jan., 22:03, Virgil <vir...@ligriv.com> wrote: > > In article > > <3e9210e4-371e-4fc4-a607-049543041...@bx10g2000vbb.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > 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. > > > > Until it is proved so by being listed, there can be legitimate doubt. > > Doubt that the terminating rationals are countable?
I know how to list all of them.
> Doubt that the definable tails are countable?
Not sure what makes a "tail", much less what makes it defineable or undefineable, so I doubt.
> Doubt that aleph_0 * aleph_0 = aleph_0?
As I have no idea what YOUR "*" means here, so I doubt.
> Not even in matheology. > > > > > An anti-diagonal cannot differ from every number of the set because > > > the set contains all numbers. > > > > Only as finite strings so that any infinite string will differ from > > every finite string. > > Not at a digit at a finite place.
Why can my string not differ from the nth finite string in your listing of finite strings in that string's nth place, if that string has one, and by having anything in my strng's nth place if your nth string is not n places long? I see no reason why my string cannot differ from each string in your whole list of strings according to such a rule. > > > > > Compare the Binary Tree where no anti- > > > diagonal can be found (in the finite realm). > > > > But the complete infinite binary tree itself does not exist in any > > finite realm, > > The complete infinite Binary Tree exists within the infinite set of > all finite levels.
Its nodes do but its paths do not.
There is no further place where it could exist. A > life after life belongs to theology. A definition afterall finite > definability belongs to matheology. > > > > > > > And there is no infinite realm. > > > > Maybe not in WMYTHEOLOGY, but there are more things in heaven and earth, > > WM, than are dreamt of your philosophy. > > Perhaps in heaven, but mathematics does not belong to heaven.
Your WMYTHEOLOGY does not even belong to Earth. > > > > > So if there are infinitely many paths > > > in the Binary Tree, then they must cross at least one finite level > > > together. > > > > Paths of finite trees don't "cross" any level together, so why should > > any other tree differ? > > All paths cross every level, but not at distinct nodes.
Each path crossed each level at a distinct node, at least if your 'level' means a fixed number of 'generations' from the root node.
> If however a > number n of paths of the Binary Tree is claimed, then ther must be a > level with n nodes.