Date: Jan 15, 2013 4:18 PM Author: mueckenh@rz.fh-augsburg.de Subject: Re: WMatheology § 191 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?

Doubt that the definable tails are countable?

Doubt that aleph_0 * aleph_0 = aleph_0?

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.

>

> > 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. 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.

>

> > 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. If however a

number n of paths of the Binary Tree is claimed, then ther must be a

level with n nodes.

>

> > 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.

>

> In a sequence of levels, either there is a last level or no last level.

>

> If there is a last level then there are only finitely many levels.

>

> If there is no last level then there are infinitely many levels.

>

> In the set of naturals numbers, beyond each natural there is another

> natural, so there more than any finite number of naturals.

Nevertheless every natural n is finite and the index n can be the last

one of a finite initial segment.

Regards, WM