Re: Cantor and the binary tree

On Thu, 23 Jun 2005 19:27:45 -0600, Virgil
<ITSnetNOTcom#virgil@xxxxxxxxxxx> wrote:

>In article <5rbmb11h2kph14fsjb57mfubs8pt5fcpm7@xxxxxxx>,
> Martin Shobe <mshobe@xxxxxxxxxxxxx> wrote:
>>
>> for finite trees this is true. For infinite trees it no longer holds.
>
>Actually, it is not even true for finite trees.
>
>For a binary tree in which every path is only one branch long, there the
>same number of paths as branches, namely 2.
>
>For a binary tree in which each path is two branches long, there are 4
>paths and 6 branches.
>
>If each path is 3 branches, there are 14 branches and 8 paths.
>
>And in general if each path in n branches there are 2^n paths and and
>2*(2^n-1) branches, which is never quite twice the number of paths.
>
>So that TO's "TWICE as many" is always wrong.

I must have had a whiff... Sorry.

Martin

.

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