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Topic: A tree with exactly one infinite path
Replies: 8   Last Post: Aug 24, 2013 12:24 PM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: A tree with exactly one infinite path
Posted: Aug 23, 2013 6:27 PM
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"Virgil" <virgil@ligriv.com> wrote in message
news:virgil-794EE9.18240822082013@BIGNEWS.USENETMONSTER.COM...
> In article <kv6452$75b$1@dont-email.me>,
> "Julio Di Egidio" <julio@diegidio.name> wrote:
>

>> "Virgil" <virgil@ligriv.com> wrote in message
>> news:virgil-75DF2B.22094321082013@BIGNEWS.USENETMONSTER.COM...
>>

>> > Consider the binary tree in which every right child has a child and
>> > every left child is a terminal node.
>> >
>> > Then there is in it for each member of |N a left terminal node having
>> > that path length, and an infinite path of all right nodes to represent
>> > the set |N itself, having one node at each length in |N.

>>
>> Just consider a unary tree.

>
> A unary tree will be a finite tree if and only if it has a terminal
> node, unlike binary trees.


You asked for a tree with exactly one infinite path, not for a tree with
terminal nodes. Indeed, as for "exact" representations of |N, what better
than an infinite (and necessarily complete) unary tree, i.e. a simple
sequence?

Julio





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