Re: Cantor and the binary tree
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Thu, 26 May 2005 11:18:15 -0600
In article <MPG.1cffa7b573ce1926989d33@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > In an infinite tree there are as many *finite* paths as nodes. Again,
> > I think you can count on general agreement (although there will be
> > some grumbling that there are infinite numbers of both and I may be
> > off by a factor of 2 but let's forget about that).
>
> If "there are as many *finite* paths as nodes", then what do the infinite
> paths
> consist of? Don't they have nodes as well? Are there infinite paths, if all
> the
> nodes are used up in the finite paths?
We can pair off the finite paths with their terminal nodes, but infinite
paths do not have terminal nodes. If we identify left-child branches
with zeros and right-child branches with ones, each infinite path can be
matched with an infinite string of zeros and ones.
.
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