Re: The complete infinite binary tree has only countably many infinite paths.
- From: LudovicoVan <julio@xxxxxxxxxxxxx>
- Date: Sat, 28 Mar 2009 09:10:47 -0700 (PDT)
On 28 Mar, 12:29, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Fri, 27 Mar 2009 13:26:20 -0700 (PDT), LudovicoVan
<ju...@xxxxxxxxxxxxx> wrote:
On 24 Mar, 11:56, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
The complete infinite binary tree has only countably many infinite
paths.
Absolutely!
not.
When the nodes are countable, how could the paths be not?
"How could they not be?"
Thanks for the correction, appreciated.
is not a proof of anything.
Indeed, it's even straightforward that there is a bijection between
the paths and the leaf nodes...
Huh? In the tree in question there are _no_ leaf nodes.
That's informal and, as such, I believe it's quite correct: easy to
see by graphical means, but you guys tend to deny any graphical
approach.
But! If you (or anybody) give a _transfinite definition_ for the
complete infinite binary tree (i.e., as near as possible to a
"constructive recipe"), then -I'll claim- giving the mentioned
bijection in formal terms is going to be trivial...
-LV
.
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