On 29 Jan 2015, at 21:50, John Clark wrote:
On Thu, Jan 29, 2015 at 2:19 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
>>> The "01" appearing above is supposed to be an initial segment
of one sequence,
>> OK, you gave me 2 elements, but what's the third element in this
uncountably infinitely long sequence of yours?
> I have never pretended that I can enumerate them. I say only that
I can generate all of them
Then generate the third element.
There is no third element.
> by dovetailing
It is not allowed to say in a algorithm "after you have completed
these infinite number of tasks then do this and such".
I would need to do to generate some special subset of the reals, not
for generating them all.
> The easyness comes from the fact that I generate them all, by
zigzagging on their initial fragment. Each initial segment is
admittedly denoting its many different precisions.
So your algorithm will have to perform a infinite number of tasks
before it gets around to finding that third element. That's no good.
There is no third element. There is no bijection between the real and
N. You know that.
> We both agree that the set of binary infinite sequences is
uncountable.
And you can't find a one to one correspondence between the set of
subsets of the Real Numbers and the Real numbers, there will always
be a subset of the Real numbers with no corresponding Real number.
Sure, but that is not the point.
Bruno
John K Clark
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