Re: abundance of irrationals!)

In article <1115724716.049455.246410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
> *** T. Winter wrote:
>
> > > Consider this List 2 please:
> > >
> > > .
> > > 0 1
> > > 0 1 0 1
> > > 0 1 0 1 0 1 0 1
> > > ...
>
> > Makes no sense. If I prepend each line by 0., and consider it as a
> > binary number, there is *no* number in that list present from the
> > interval [1/2, 1).
>
> What about 2/3 = 0.101010...?
>
> (a_n) = 2_1, 3_2, 6_3

Still makes not much sense to me. What does the list list. Single digits?
And is the purpose to have such a list that for each number in [0,1)
subsequent digits of that number can be found at increasing places in
your list? In that case (in binary) the list 0101010101... would do
just as well.

> > Pray rephrase your definition of the list so that it makes sense.
>
> A more suggestive notation is (please use Courier or equivalent
> constant spacing types):
>
> .
> 0 1
> 0 1 0 1
> 0 1 0 1 0 1 0 1

Ah, I think I see what you mean. I think that your list is not a
list but a binary tree, and that when you follow a branch you will
find a number at the end, and you will eventually find every number
in [0,1) this way. And I *think* that you claim that the number of
branches is countable. Can you prove that?
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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