Re: Approaching the infinite binary tree

On Oct 1, 8:12 am, LudovicoVan <ju...@xxxxxxxxxxxxx> wrote:
On 29 Sep, 05:04, "Salviati" <eckard.blumsch...@xxxxxxxx> wrote:



"LudovicoVan" <ju...@xxxxxxxxxxxxx> schrieb im Newsbeitragnews:85a88c3e-0e26-4b34-9c7c-5f5b7645ec71@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>Iam thinking along the following lines, and I'd greatly appreciate
some feedback.

Given the set of the extended naturals: N* := N u {w}, where
'w' (omega) is the limit ordinal.

...

The number of points on a diagonal at step k is 2^k, and they delimit
(2^k)-1 equal intervals, each of (normalized) length equal to 1/
[(2^k)-1]. In the limit case we can -informally- say that we have 2^w
limit points delimiting (2^w)-1 equal intervals, each of length 1/
[(2^w)-1]. With the theory of IFS we can prove (I won't try) that a
distance function expressed in these geometrical terms provides a
*complete* metric space.

The last one I recall who dealt with the infinite binary tree was W.M.
Did you read his (second) booklet?

I have found his articles on arxiv and it seems not there:http://arxiv.org/find/all/1/au:+Mueckenheim/0/1/0/all/0/1

Particularly amusing is <http://arxiv.org/abs/math/0305310>,
which shows that there is no bijection between
the set of natural numbers and itself.

-- m
.

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