Re: Cantor and the binary tree

imaginatorium@xxxxxxxxxxxxx said:
>
>
> Tony Orlow (aeo6) wrote:
>
> <snip> ... Here it is again, the standard 'argument':

That was an obnoxious snip. You deliberately snipped the context, where Martin
said:

> What is it you are smoking? Can I have some? Even in finite binary
> trees, the number of paths is greater than the number of nodes where
> branching occurs.
>
This is a statement specifically about FINITE binary trees, and it's incorrect.
Try to be honest from now on, and stop snipping context to make others look
stupid.

>
> > Excuse me Martin, but maybe you should have some of what I am smoking. Every
> > path ends in a leaf node, which are half the nodes in the tree.
>
> An infinite tree means one in which *every* node branches and leads to
> more paths. However, in a *finite* tree, every path ends in a leaf
> node. In real mathematics that means that in an infinite tree, every
> path is unending. But in Orlovian mathematics, any selected statement
> true of a finite object is also true of an infinite one, and therefore,
> although the paths never end, they end in leaf nodes.
Do you see how this statement sounds in the context of what you snipped? Yep,
pretty dumb.

>
> > ... You start with
> > one node that represents the root path. For each pair of nodes, you create a
> > new path. A finite tree with n levels (including the root) has (2^n)-1 nodes,
> > (2^n)-2 branches, and only 2^(n-1), or (2^n)/2 paths, as denoted by its leaf
> > nodes. This relationship is preserved through infinity, even in the absence of
> > identifiable leaf nodes.
>
> Say the magic Induction Mantra "Preserved through infinity", and
> overcome the nonexistence of something by claiming it is
> "unidentifiable".
>
> Hmm. Seen it all before, somewhere.
Probably somewhere else where it didn't exist. You want to get that checked
out. I hear there's a cure for Cantorian flu......
>
> Brian Chandler
> http://imaginatorium.org
>
>

--
Smiles,

Tony
.

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