Re: Cantor and the binary tree



Tony Orlow (aeo6) wrote:

<snip> ... Here it is again, the standard 'argument':

> 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.

> ... 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.

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

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  • Re: Cantor and the binary tree
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