Virgil
Posts:
4,666
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 4, 2013 6:14 PM
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In article <tbCdnURtDtB9so3MnZ2dnUVZ_sWdnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:
>
> From the beginning (I showed up when Zuhair was asking questions)
> I have not understood terminology. A CIBT is the Cantor space.
> It is a topological construct and the C refers to topological
> completeness.
In my disputes with WM, a "CIBT" or "COMPLETE INFINITE BINARY TREE"
is a countably infinite set of nodes, with a unique root node and such
that every node has two child nodes, a "left child" and a "right child",
and every node but the root node has one parent node for which it is
either a left child or a right child.
One can model it with its nodes being positive naturals:
1
/ \
/ \
2 3
/ \ / \
4 5 6 7
/ \ / \ / \ / \
So that the left child of any node n is 2*n and its right child is
2*n+1, and the parent of any node n except 1 is floor(n/2).
>
> Of course, many logicians work primarily with logical
> constructs involving discrete alphabets. So, I assume
> that I am just misunderstanding the jargon of a
> particular branch of mathematicians.
>
> I do not include WM's uses in that remark. While I
> understand his objections, I am still trying to understand
> some of his statements.
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